diff --git a/search.json b/search.json
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+++ b/search.json
@@ -69,7 +69,7 @@
"href": "vignettes/spatial.html#estimating-the-model",
"title": "Spatial Effects",
"section": "5 Estimating the Model",
- "text": "5 Estimating the Model\nWe now estimate the spatial count model using the Negative Binomial distribution (NBI). The model includes smooth functions of altitude, year, and an interaction between altitude and year, as well as a (functional) random effect over regions for the time trend. Spatial effects are incorporated using the bs = \"mrf\" option.\n\n## estimate count model using the NBI family,\n## model formula is\nf <- ~ s(log(alt + 10)) + s(year) + s(id, bs = \"mrf\", xt = list(\"penalty\" = K), k = 100)\nf <- list(update(f, counts ~ .), f)\n\n## estimate model using BIC for shrinkage parameter selection\nb <- gamlss2(f, data = storms, family = NBI, criterion = \"BIC\")\n\nNote that estimation of this model takes some time, because of the quite high number of coefficients for the (functional) random effect ti(id, year, bs = c(\"re\", \"cr\"), k = c(157, 5)).\n\n## model summary\nsummary(b)\n\nCall:\ngamlss2(formula = counts ~ s(log(alt + 10)) + s(year) + s(id, \n bs = \"mrf\", xt = list(penalty = K), k = 100) | s(log(alt + \n 10)) + s(year) + s(id, bs = \"mrf\", xt = list(penalty = K), \n k = 100), data = storms, family = NBI, ... = pairlist(x = FALSE, criterion = \"BIC\"))\n---\nFamily: NBI \nLink function: mu = log, sigma = log\n*--------\nParameter: mu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 1.2999 0.0167 77.86 <2e-16 ***\n---\nSmooth terms:\n s(log(alt + 10)) s(year) s(id)\nedf 7.5077 2.2994 52.88\n*--------\nParameter: sigma \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -0.20330 0.02505 -8.117 6.6e-16 ***\n---\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n---\nSmooth terms:\n s(log(alt + 10)) s(year) s(id)\nedf 7.4533 2.1207 24.712\n*--------\nn = 3494 df = 98.97 res.df = 3395.03\nDeviance = 16484.181 Null Dev. Red. = 14.46%\nAIC = 16682.1271 elapsed = 4.40sec\n\n\nModel calibration is checked using histogram, Q-Q plot, wormplot etc.\n\nplot(b, which = \"resid\")\n\n\n\n\n\n\n\n\nHere, the spatial effect is modeled as an MRF smooth (s(id, bs = \"mrf\")), where the penalty matrix K enforces spatial structure based on neighboring stations. We use the Bayesian Information Criterion (BIC) to select the optimal smoothing parameters.",
+ "text": "5 Estimating the Model\nWe now estimate the spatial count model using the Negative Binomial distribution (NBI). The model includes smooth functions of altitude, year, and an interaction between altitude and year, as well as a (functional) random effect over regions for the time trend. Spatial effects are incorporated using the bs = \"mrf\" option.\n\n## estimate count model using the NBI family,\n## model formula is\nf <- ~ s(log(alt + 10)) + s(year) + s(id, bs = \"mrf\", xt = list(\"penalty\" = K), k = 100)\nf <- list(update(f, counts ~ .), f)\n\n## estimate model using BIC for shrinkage parameter selection\nb <- gamlss2(f, data = storms, family = NBI, criterion = \"BIC\")\n\nNote that estimation of this model takes some time, because of the quite high number of coefficients for the (functional) random effect ti(id, year, bs = c(\"re\", \"cr\"), k = c(157, 5)).\n\n## model summary\nsummary(b)\n\nCall:\ngamlss2(formula = counts ~ s(log(alt + 10)) + s(year) + s(id, \n bs = \"mrf\", xt = list(penalty = K), k = 100) | s(log(alt + \n 10)) + s(year) + s(id, bs = \"mrf\", xt = list(penalty = K), \n k = 100), data = storms, family = NBI, ... = pairlist(x = FALSE, criterion = \"BIC\"))\n---\nFamily: NBI \nLink function: mu = log, sigma = log\n*--------\nParameter: mu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 1.2999 0.0167 77.86 <2e-16 ***\n---\nSmooth terms:\n s(log(alt + 10)) s(year) s(id)\nedf 7.5077 2.2994 52.88\n*--------\nParameter: sigma \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -0.20330 0.02505 -8.117 6.6e-16 ***\n---\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n---\nSmooth terms:\n s(log(alt + 10)) s(year) s(id)\nedf 7.4533 2.1207 24.712\n*--------\nn = 3494 df = 98.97 res.df = 3395.03\nDeviance = 16484.181 Null Dev. Red. = 14.46%\nAIC = 16682.1271 elapsed = 4.35sec\n\n\nModel calibration is checked using histogram, Q-Q plot, wormplot etc.\n\nplot(b, which = \"resid\")\n\n\n\n\n\n\n\n\nHere, the spatial effect is modeled as an MRF smooth (s(id, bs = \"mrf\")), where the penalty matrix K enforces spatial structure based on neighboring stations. We use the Bayesian Information Criterion (BIC) to select the optimal smoothing parameters.",
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"Articles",
"Spatial Effects"
@@ -113,7 +113,7 @@
"href": "vignettes/s_pb.html",
"title": "Smooth Terms using s() and pb()",
"section": "",
- "text": "Examples on how to set up models using smooth terms with s() and pb().\n\n\n\n\nReferences\n\nEilers, P. H. C., and B. D. Marx. 2021. Practical Smoothing: The Joys of p-Splines. Cambridge University Press.\n\n\nFahrmeir, Ludwig, Thomas Kneib, Stefan Lang, and Brian Marx. 2021. Regression – Models, Methods and Applications. 2nd ed. Berlin: Springer-Verlag. https://doi.org/10.1007/978-3-662-63882-8.\n\n\nHofner, B., A. Mayr, N. Robinzonov, and M. Schmid. 2014. “Model-Based Boosting in R: A Hands-on Tutorial Using the R Package mboost.” Computational Statistics 29: 3–35. https://doi.org/10.1007/s00180-012-0382-5.\n\n\nHofner, B., A. Mayr, and M. Schmid. 2016. “gamboostLSS: An R Package for Model Building and Variable Selection in the GAMLSS Framework.” Journal of Statistical Software 74 (1): 1–31. https://doi.org/10.18637/jss.v074.i01.\n\n\nKleiber, C., and A. Zeileis. 2016. “Visualizing Count Data Regressions Using Rootograms.” The American Statistician 70 (3): 296–303. https://doi.org/10.1080/00031305.2016.1173590.\n\n\nLang, Stefan, Nikolaus Umlauf, Peter Wechselberger, Kenneth Harttgen, and Thomas Kneib. 2012. “Multilevel Structured Additive Regression.” Statistics and Computing 24 (2): 223–38. https://doi.org/10.1007/s11222-012-9366-0.\n\n\nMayr, A., N. Fenske, B. Hofner, T. Kneib, and M. Schmid. 2012. “Generalized Additive Models for Location, Scale and Shape for High Dimensional Data, a Flexible Approach Based on Boosting.” Journal of the Royal Statistical Society C 61: 403–27. https://doi.org/10.1111/j.1467-9876.2011.01033.x.\n\n\nRigby, R. A., and D. M. Stasinopoulos. 2005. “Generalized Additive Models for Location, Scale and Shape.” Journal of the Royal Statistical Society C 54 (3): 507–54. https://doi.org/10.1111/j.1467-9876.2005.00510.x.\n\n\nRigby, R. A., D. M. Stasinopoulos, G. Z. Heller, and F. De Bastiani. 2019. Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R. Boca Raton: Chapman & Hall/CRC.\n\n\nStadlmann, S. 2019. Distreg.vis: Framework for the Visualization of Distributional Regression Models. https://doi.org/10.32614/CRAN.package.distreg.vis.\n\n\nStasinopoulos, D. M., R. A. Rigby, and F. De Bastiani. 2018. “GAMLSS: A Distributional Regression Approach.” Statistical Modelling 18 (3-4): 248–73. https://doi.org/10.1177/1471082x18759144.\n\n\nStasinopoulos, D. M., R. A. Rigby, N. Giorgikopoulos, and F. De Bastiani. 2022. “Principal Component Regression in GAMLSS Applied to Greek-German Government Bond Yield Spreads.” Statistical Modelling 22 (1-2): 127–45. https://doi.org/10.1177/1471082x211022980.\n\n\nStasinopoulos, D. M., R. A. Rigby, G. Z. Heller, V. Voudouris, and F. De Bastiani. 2017. Flexible Regression and Smoothing: Using GAMLSS in R. Boca Raton: Chapman & Hall/CRC. https://doi.org/10.1201/b21973.\n\n\nStasinopoulos, Dimitrios M, Robert A Rigby, Gillian Z Heller, and Fernanda De Bastiani. 2023. “P-Splines and GAMLSS: A Powerful Combination, with an Application to Zero-Adjusted Distributions.” Statistical Modelling 23 (5-6): 510–24. https://doi.org/10.1177/1471082x231176635.\n\n\nStasinopoulos, M. D., T. Kneib, N. Klein, A. Mayr, and G. Z Heller. 2024. Generalized Additive Models for Location, Scale and Shape: A Distributional Regression Approach, with Applications. Vol. 56. Cambridge University Press.\n\n\nUmlauf, N., N. Klein, and A. Zeileis. 2018. “BAMLSS: Bayesian Additive Models for Location, Scale and Shape (and Beyond).” Journal of Computational and Graphical Statistics 27 (3): 612–27. https://doi.org/10.1080/10618600.2017.1407325.",
+ "text": "Examples on how to set up models using smooth terms with s() and pb().\n\n\n\n\nReferences\n\nEilers, P. H. C., and B. D. Marx. 2021. Practical Smoothing: The Joys of p-Splines. Cambridge University Press.\n\n\nFahrmeir, Ludwig, Thomas Kneib, Stefan Lang, and Brian Marx. 2021. Regression – Models, Methods and Applications. 2nd ed. Berlin: Springer-Verlag. https://doi.org/10.1007/978-3-662-63882-8.\n\n\nHofner, B., A. Mayr, N. Robinzonov, and M. Schmid. 2014. “Model-Based Boosting in r: A Hands-on Tutorial Using the r Package Mboost.” Computational Statistics 29: 3–35.\n\n\nHofner, B., A. Mayr, and M. Schmid. 2016. “gamboostLSS: An R Package for Model Building and Variable Selection in the GAMLSS Framework.” Journal of Statistical Software 74 (1): 1–31.\n\n\nKleiber, C., and A. Zeileis. 2016. “Visualizing Count Data Regressions Using Rootograms.” The American Statistician 70 (3): 296–303.\n\n\nLang, Stefan, Nikolaus Umlauf, Peter Wechselberger, Kenneth Harttgen, and Thomas Kneib. 2012. “Multilevel Structured Additive Regression.” Statistics and Computing 24 (2): 223–38. https://doi.org/10.1007/s11222-012-9366-0.\n\n\nMayr, A., N. Fenske, B. Hofner, T. Kneib, and M. Schmid. 2012. “Generalized Additive Models for Location, Scale and Shape for High Dimensional Data, a Flexible Approach Based on Boosting.” J. R. Statist. Soc. Series C 61: 403–27.\n\n\nRigby, R. A., and D. M. Stasinopoulos. 2005. “Generalized Additive Models for Location, Scale and Shape.” Journal of the Royal Statistical Society C 54 (3): 507–54. https://doi.org/10.1111/j.1467-9876.2005.00510.x.\n\n\nRigby, R. A., D. M. Stasinopoulos, G. Z. Heller, and F. De Bastiani. 2019. Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R. Boca Raton: Chapman & Hall/CRC. https://doi.org/10.1201/9780429298547.\n\n\nStadlmann, S. 2019. Distreg.vis: Framework for the Visualization of Distributional Regression Models. https://CRAN.R-project.org/package=distreg.vis.\n\n\nStasinopoulos, D. M., R. A. Rigby, and F. De Bastiani. 2018. “GAMLSS: A Distributional Regression Approach.” Statistical Modelling 18 (3-4): 248–73.\n\n\nStasinopoulos, D. M., R. A. Rigby, N. Giorgikopoulos, and F. De Bastiani. 2022. “Principal Component Regression in GAMLSS Applied to Greek-German Government Bond Yield Spreads.” Statistical Modelling 22 (1-2): 127–45. https://doi.org/10.1177/1471082x211022980.\n\n\nStasinopoulos, D. M., R. A. Rigby, G. Z. Heller, V. Voudouris, and F. De Bastiani. 2017. Flexible Regression and Smoothing: Using GAMLSS in r. Boca Raton: Chapman & Hall/CRC.\n\n\nStasinopoulos, Dimitrios M, Robert A Rigby, Gillian Z Heller, and Fernanda De Bastiani. 2023. “P-Splines and GAMLSS: A Powerful Combination, with an Application to Zero-Adjusted Distributions.” Statistical Modelling 23 (5-6): 510–24.\n\n\nStasinopoulos, M. D., T. Kneib, N. Klein, A. Mayr, and G. Z Heller. 2024. Generalized Additive Models for Location, Scale and Shape: A Distributional Regression Approach, with Applications. Vol. 56. Cambridge University Press.\n\n\nUmlauf, N., N. Klein, and A. Zeileis. 2018. “BAMLSS: Bayesian Additive Models for Location, Scale and Shape (and Beyond).” Journal of Computational and Graphical Statistics 27 (3): 612–27. https://doi.org/10.1080/10618600.2017.1407325.",
"crumbs": [
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"Smooth Terms using s() and pb()"
@@ -365,7 +365,7 @@
"href": "man/gamlss2.html",
"title": "gamlss2",
"section": "",
- "text": "Estimation of generalized additive models for location scale and shape (GAMLSS). The model fitting function gamlss2() provides flexible infrastructures to estimate the parameters of a response distribution. The number of distributional parameters is not fixed, see gamlss2.family. Moreover, gamlss2() supports all smooth term constructors from the mgcv package in addition to the classical model terms as provided by gamlss and gamlss.add.\n\n\n\ngamlss2(x, ...)\n\n## S3 method for class 'formula'\ngamlss2(formula, data, family = NO,\n subset, na.action, weights, offset, start = NULL,\n control = gamlss2_control(...), ...)\n\n## S3 method for class 'list'\ngamlss2(x, ...)\n\n\n\n\n\n\n\nformula\n\n\nA GAM-type formula or Formula. All smooth terms of the mgcv package are supported, see also formula.gam.\n\n\n\n\nx\n\n\nFor gamlss.list() x is a list of formulas.\n\n\n\n\ndata\n\n\nA data frame or list or environment containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which gamlss2 is called.\n\n\n\n\nfamily\n\n\nA gamlss.family or gamlss2.family object used to define distribution and the link functions of the parameters.\n\n\n\n\nsubset\n\n\nAn optional vector specifying a subset of observations to be used in the fitting process.\n\n\n\n\nna.action\n\n\nNA processing for setting up the model.frame.\n\n\n\n\nweights\n\n\nAn optional vector of prior weights to be used in the fitting process. Should be NULL or a numeric vector.\n\n\n\n\noffset\n\n\nThis can be used to specify an a priori known components to be included in the linear predictors during fitting. Please note that if only a single numeric vector is provided, the offset will be assigned to the first specified parameter of the distribution. In the case of multiple offsets, a data frame or list must be supplied. Each offset is assigned in the same order as the parameters of the distribution specified in the family object.\n\n\n\n\nstart\n\n\nStarting values for estimation algorithms.\n\n\n\n\ncontrol\n\n\nA list of control arguments, see gamlss2_control.\n\n\n\n\n…\n\n\nArguments passed to gamlss2_control.\n\n\n\n\n\n\nThe model fitting function gamlss2() provides flexible infrastructures for the estimation of GAMLSS.\n\n\nDistributional models are specified using family objects, either from the gamlss.dist package or using gamlss2.family objects.\n\n\nEstimation is carried out through a Newton-Raphson/Fisher scoring algorithm, see function RS. The estimation algorithms can also be exchanged using gamlss2_control. Additionally, if an optimizer is specified by the family object, this optimizer function will be employed for estimation.\n\n\nThe return value is determined by the object returned from the optimizer function, typically an object of class “gamlss2”. Default methods and extractor functions are available for this class. Nevertheless, users have the flexibility to supply their own optimizer function, along with user-specific methods tailored for the returned object.\n\n\n\n\n\nThe return value is determined by the object returned from the optimizer function. By default, the optimization is performed using the RS optimizer function (see gamlss2_control), yielding an object of class “gamlss2”. Default methods and extractor functions are available for this class.\n\n\n\nRigby RA, Stasinopoulos DM (2005). “Generalized Additive Models for Location, Scale and Shape (with Discussion).” Journal of the Royal Statistical Society, Series C (Applied Statistics), 54, 507–554. doi:10.1111/j.1467-9876.2005.00510.x\nRigby RA, Stasinopoulos DM, Heller GZ, De Bastiani F (2019). Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/9780429298547\nStasinopoulos DM, Rigby RA (2007). “Generalized Additive Models for Location Scale and Shape (GAMLSS) in R.” Journal of Statistical Software, 23(7), 1–46. doi:10.18637/jss.v023.i07\nStasinopoulos DM, Rigby RA, Heller GZ, Voudouris V, De Bastiani F (2017). Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/b21973\n\n\n\nRS, gamlss2_control, gamlss2.family\n\n\n\n\nlibrary(\"gamlss2\")\n\n\n## load the abdominal circumference data\ndata(\"abdom\", package = \"gamlss.data\")\n\n## specify the model Formula\nf <- y ~ s(x) | s(x) | s(x) | s(x)\n\n## estimate model\nb <- gamlss2(f, data = abdom, family = BCT)\n\nGAMLSS-RS iteration 1: Global Deviance = 4774.4683 eps = 0.534345 \nGAMLSS-RS iteration 2: Global Deviance = 4770.229 eps = 0.000887 \nGAMLSS-RS iteration 3: Global Deviance = 4770.1663 eps = 0.000013 \nGAMLSS-RS iteration 4: Global Deviance = 4770.1554 eps = 0.000002 \n\n## model summary\nsummary(b)\n\nCall:\ngamlss2(formula = f, data = abdom, family = BCT)\n---\nFamily: BCT \nLink function: mu = identity, sigma = log, nu = identity, tau = log\n*--------\nParameter: mu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 226.334 1.257 180 <2e-16 ***\n---\nSmooth terms:\n s(x)\nedf 4.551\n*--------\nParameter: sigma \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -2.92264 0.01101 -265.5 <2e-16 ***\n---\nSmooth terms:\n s(x)\nedf 2.5639\n*--------\nParameter: nu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -0.18021 0.04599 -3.918 9.95e-05 ***\n---\nSmooth terms:\n s(x)\nedf 1.0015\n*--------\nParameter: tau \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 2.6548 0.0144 184.4 <2e-16 ***\n---\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n---\nSmooth terms:\n s(x)\nedf 1.0042\n*--------\nn = 610 df = 13.12 res.df = 596.88\nDeviance = 4770.1554 Null Dev. Red. = 33.39%\nAIC = 4796.3966 elapsed = 0.78sec\n\n## plot estimated effects\nplot(b, which = \"effects\")\n\n\n\n\n\n\n\n## plot diagnostics\nplot(b, which = \"resid\")\n\n\n\n\n\n\n\n## predict parameters\npar <- predict(b)\n\n## predict quantiles\npq <- sapply(c(0.05, 0.5, 0.95), function(q) family(b)$q(q, par))\n\n## visualize\nplot(y ~ x, data = abdom, pch = 19,\n col = rgb(0.1, 0.1, 0.1, alpha = 0.3))\nmatplot(abdom$x, pq, type = \"l\", lwd = 2,\n lty = 1, col = 4, add = TRUE)\n\n\n\n\n\n\n\n## use of starting values\nm <- gamlss2(f, data = abdom, family = BCT,\n start = c(mu = 200, sigma = 0.1, nu = 0, tau = 10))\n\nGAMLSS-RS iteration 1: Global Deviance = 4789.7797 eps = 0.556012 \nGAMLSS-RS iteration 2: Global Deviance = 4774.5657 eps = 0.003176 \nGAMLSS-RS iteration 3: Global Deviance = 4771.4193 eps = 0.000658 \nGAMLSS-RS iteration 4: Global Deviance = 4769.9947 eps = 0.000298 \nGAMLSS-RS iteration 5: Global Deviance = 4769.9556 eps = 0.000008 \n\n## fix some parameters\nm <- gamlss2(f, data = abdom, family = BCT,\n start = c(mu = 200, sigma = 0.1, nu = 0, tau = 10),\n fixed = c(nu = TRUE, tau = TRUE))\n\nGAMLSS-RS iteration 1: Global Deviance = 4799.422 eps = 0.555118 \nGAMLSS-RS iteration 2: Global Deviance = 4795.2807 eps = 0.000862 \nGAMLSS-RS iteration 3: Global Deviance = 4795.2668 eps = 0.000002 \n\n## estimated coefficients (intercepts)\ncoef(m)\n\n mu.p.(Intercept) sigma.p.(Intercept) nu.p.(Intercept) tau.p.(Intercept) \n 226.347632 -2.922923 0.000000 2.302585 \n\n## starting values using full predictors\nm <- gamlss2(f, data = abdom, family = BCT,\n start = fitted(m))\n\nGAMLSS-RS iteration 1: Global Deviance = 4902.0767 eps = 0.372276 \nGAMLSS-RS iteration 2: Global Deviance = 4775.8465 eps = 0.025750 \nGAMLSS-RS iteration 3: Global Deviance = 4775.0302 eps = 0.000170 \nGAMLSS-RS iteration 4: Global Deviance = 4774.9582 eps = 0.000015 \nGAMLSS-RS iteration 5: Global Deviance = 4774.9519 eps = 0.000001 \n\n## same with\nm <- gamlss2(f, data = abdom, family = BCT,\n start = m)\n\nGAMLSS-RS iteration 1: Global Deviance = 4774.4683 eps = 0.534345 \nGAMLSS-RS iteration 2: Global Deviance = 4770.229 eps = 0.000887 \nGAMLSS-RS iteration 3: Global Deviance = 4770.1663 eps = 0.000013 \nGAMLSS-RS iteration 4: Global Deviance = 4770.1554 eps = 0.000002",
+ "text": "Estimation of generalized additive models for location scale and shape (GAMLSS). The model fitting function gamlss2() provides flexible infrastructures to estimate the parameters of a response distribution. The number of distributional parameters is not fixed, see gamlss2.family. Moreover, gamlss2() supports all smooth term constructors from the mgcv package in addition to the classical model terms as provided by gamlss and gamlss.add.\n\n\n\ngamlss2(x, ...)\n\n## S3 method for class 'formula'\ngamlss2(formula, data, family = NO,\n subset, na.action, weights, offset, start = NULL,\n control = gamlss2_control(...), ...)\n\n## S3 method for class 'list'\ngamlss2(x, ...)\n\n\n\n\n\n\n\nformula\n\n\nA GAM-type formula or Formula. All smooth terms of the mgcv package are supported, see also formula.gam.\n\n\n\n\nx\n\n\nFor gamlss.list() x is a list of formulas.\n\n\n\n\ndata\n\n\nA data frame or list or environment containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which gamlss2 is called.\n\n\n\n\nfamily\n\n\nA gamlss.family or gamlss2.family object used to define distribution and the link functions of the parameters.\n\n\n\n\nsubset\n\n\nAn optional vector specifying a subset of observations to be used in the fitting process.\n\n\n\n\nna.action\n\n\nNA processing for setting up the model.frame.\n\n\n\n\nweights\n\n\nAn optional vector of prior weights to be used in the fitting process. Should be NULL or a numeric vector.\n\n\n\n\noffset\n\n\nThis can be used to specify an a priori known components to be included in the linear predictors during fitting. Please note that if only a single numeric vector is provided, the offset will be assigned to the first specified parameter of the distribution. In the case of multiple offsets, a data frame or list must be supplied. Each offset is assigned in the same order as the parameters of the distribution specified in the family object.\n\n\n\n\nstart\n\n\nStarting values for estimation algorithms.\n\n\n\n\ncontrol\n\n\nA list of control arguments, see gamlss2_control.\n\n\n\n\n…\n\n\nArguments passed to gamlss2_control.\n\n\n\n\n\n\nThe model fitting function gamlss2() provides flexible infrastructures for the estimation of GAMLSS.\n\n\nDistributional models are specified using family objects, either from the gamlss.dist package or using gamlss2.family objects.\n\n\nEstimation is carried out through a Newton-Raphson/Fisher scoring algorithm, see function RS. The estimation algorithms can also be exchanged using gamlss2_control. Additionally, if an optimizer is specified by the family object, this optimizer function will be employed for estimation.\n\n\nThe return value is determined by the object returned from the optimizer function, typically an object of class “gamlss2”. Default methods and extractor functions are available for this class. Nevertheless, users have the flexibility to supply their own optimizer function, along with user-specific methods tailored for the returned object.\n\n\n\n\n\nThe return value is determined by the object returned from the optimizer function. By default, the optimization is performed using the RS optimizer function (see gamlss2_control), yielding an object of class “gamlss2”. Default methods and extractor functions are available for this class.\n\n\n\nRigby RA, Stasinopoulos DM (2005). “Generalized Additive Models for Location, Scale and Shape (with Discussion).” Journal of the Royal Statistical Society, Series C (Applied Statistics), 54, 507–554. doi:10.1111/j.1467-9876.2005.00510.x\nRigby RA, Stasinopoulos DM, Heller GZ, De Bastiani F (2019). Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/9780429298547\nStasinopoulos DM, Rigby RA (2007). “Generalized Additive Models for Location Scale and Shape (GAMLSS) in R.” Journal of Statistical Software, 23(7), 1–46. doi:10.18637/jss.v023.i07\nStasinopoulos DM, Rigby RA, Heller GZ, Voudouris V, De Bastiani F (2017). Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/b21973\n\n\n\nRS, gamlss2_control, gamlss2.family\n\n\n\n\nlibrary(\"gamlss2\")\n\n\n## load the abdominal circumference data\ndata(\"abdom\", package = \"gamlss.data\")\n\n## specify the model Formula\nf <- y ~ s(x) | s(x) | s(x) | s(x)\n\n## estimate model\nb <- gamlss2(f, data = abdom, family = BCT)\n\nGAMLSS-RS iteration 1: Global Deviance = 4774.4683 eps = 0.534345 \nGAMLSS-RS iteration 2: Global Deviance = 4770.229 eps = 0.000887 \nGAMLSS-RS iteration 3: Global Deviance = 4770.1663 eps = 0.000013 \nGAMLSS-RS iteration 4: Global Deviance = 4770.1554 eps = 0.000002 \n\n## model summary\nsummary(b)\n\nCall:\ngamlss2(formula = f, data = abdom, family = BCT)\n---\nFamily: BCT \nLink function: mu = identity, sigma = log, nu = identity, tau = log\n*--------\nParameter: mu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 226.334 1.257 180 <2e-16 ***\n---\nSmooth terms:\n s(x)\nedf 4.551\n*--------\nParameter: sigma \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -2.92264 0.01101 -265.5 <2e-16 ***\n---\nSmooth terms:\n s(x)\nedf 2.5639\n*--------\nParameter: nu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -0.18021 0.04599 -3.918 9.95e-05 ***\n---\nSmooth terms:\n s(x)\nedf 1.0015\n*--------\nParameter: tau \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 2.6548 0.0144 184.4 <2e-16 ***\n---\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n---\nSmooth terms:\n s(x)\nedf 1.0042\n*--------\nn = 610 df = 13.12 res.df = 596.88\nDeviance = 4770.1554 Null Dev. Red. = 33.39%\nAIC = 4796.3966 elapsed = 0.77sec\n\n## plot estimated effects\nplot(b, which = \"effects\")\n\n\n\n\n\n\n\n## plot diagnostics\nplot(b, which = \"resid\")\n\n\n\n\n\n\n\n## predict parameters\npar <- predict(b)\n\n## predict quantiles\npq <- sapply(c(0.05, 0.5, 0.95), function(q) family(b)$q(q, par))\n\n## visualize\nplot(y ~ x, data = abdom, pch = 19,\n col = rgb(0.1, 0.1, 0.1, alpha = 0.3))\nmatplot(abdom$x, pq, type = \"l\", lwd = 2,\n lty = 1, col = 4, add = TRUE)\n\n\n\n\n\n\n\n## use of starting values\nm <- gamlss2(f, data = abdom, family = BCT,\n start = c(mu = 200, sigma = 0.1, nu = 0, tau = 10))\n\nGAMLSS-RS iteration 1: Global Deviance = 4789.7797 eps = 0.556012 \nGAMLSS-RS iteration 2: Global Deviance = 4774.5657 eps = 0.003176 \nGAMLSS-RS iteration 3: Global Deviance = 4771.4193 eps = 0.000658 \nGAMLSS-RS iteration 4: Global Deviance = 4769.9947 eps = 0.000298 \nGAMLSS-RS iteration 5: Global Deviance = 4769.9556 eps = 0.000008 \n\n## fix some parameters\nm <- gamlss2(f, data = abdom, family = BCT,\n start = c(mu = 200, sigma = 0.1, nu = 0, tau = 10),\n fixed = c(nu = TRUE, tau = TRUE))\n\nGAMLSS-RS iteration 1: Global Deviance = 4799.422 eps = 0.555118 \nGAMLSS-RS iteration 2: Global Deviance = 4795.2807 eps = 0.000862 \nGAMLSS-RS iteration 3: Global Deviance = 4795.2668 eps = 0.000002 \n\n## estimated coefficients (intercepts)\ncoef(m)\n\n mu.p.(Intercept) sigma.p.(Intercept) nu.p.(Intercept) tau.p.(Intercept) \n 226.347632 -2.922923 0.000000 2.302585 \n\n## starting values using full predictors\nm <- gamlss2(f, data = abdom, family = BCT,\n start = fitted(m))\n\nGAMLSS-RS iteration 1: Global Deviance = 4902.0767 eps = 0.372276 \nGAMLSS-RS iteration 2: Global Deviance = 4775.8465 eps = 0.025750 \nGAMLSS-RS iteration 3: Global Deviance = 4775.0302 eps = 0.000170 \nGAMLSS-RS iteration 4: Global Deviance = 4774.9582 eps = 0.000015 \nGAMLSS-RS iteration 5: Global Deviance = 4774.9519 eps = 0.000001 \n\n## same with\nm <- gamlss2(f, data = abdom, family = BCT,\n start = m)\n\nGAMLSS-RS iteration 1: Global Deviance = 4774.4683 eps = 0.534345 \nGAMLSS-RS iteration 2: Global Deviance = 4770.229 eps = 0.000887 \nGAMLSS-RS iteration 3: Global Deviance = 4770.1663 eps = 0.000013 \nGAMLSS-RS iteration 4: Global Deviance = 4770.1554 eps = 0.000002",
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- "text": "Estimation of generalized additive models for location scale and shape (GAMLSS). The model fitting function gamlss2() provides flexible infrastructures to estimate the parameters of a response distribution. The number of distributional parameters is not fixed, see gamlss2.family. Moreover, gamlss2() supports all smooth term constructors from the mgcv package in addition to the classical model terms as provided by gamlss and gamlss.add.\n\n\n\ngamlss2(x, ...)\n\n## S3 method for class 'formula'\ngamlss2(formula, data, family = NO,\n subset, na.action, weights, offset, start = NULL,\n control = gamlss2_control(...), ...)\n\n## S3 method for class 'list'\ngamlss2(x, ...)\n\n\n\n\n\n\n\nformula\n\n\nA GAM-type formula or Formula. All smooth terms of the mgcv package are supported, see also formula.gam.\n\n\n\n\nx\n\n\nFor gamlss.list() x is a list of formulas.\n\n\n\n\ndata\n\n\nA data frame or list or environment containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which gamlss2 is called.\n\n\n\n\nfamily\n\n\nA gamlss.family or gamlss2.family object used to define distribution and the link functions of the parameters.\n\n\n\n\nsubset\n\n\nAn optional vector specifying a subset of observations to be used in the fitting process.\n\n\n\n\nna.action\n\n\nNA processing for setting up the model.frame.\n\n\n\n\nweights\n\n\nAn optional vector of prior weights to be used in the fitting process. Should be NULL or a numeric vector.\n\n\n\n\noffset\n\n\nThis can be used to specify an a priori known components to be included in the linear predictors during fitting. Please note that if only a single numeric vector is provided, the offset will be assigned to the first specified parameter of the distribution. In the case of multiple offsets, a data frame or list must be supplied. Each offset is assigned in the same order as the parameters of the distribution specified in the family object.\n\n\n\n\nstart\n\n\nStarting values for estimation algorithms.\n\n\n\n\ncontrol\n\n\nA list of control arguments, see gamlss2_control.\n\n\n\n\n…\n\n\nArguments passed to gamlss2_control.\n\n\n\n\n\n\nThe model fitting function gamlss2() provides flexible infrastructures for the estimation of GAMLSS.\n\n\nDistributional models are specified using family objects, either from the gamlss.dist package or using gamlss2.family objects.\n\n\nEstimation is carried out through a Newton-Raphson/Fisher scoring algorithm, see function RS. The estimation algorithms can also be exchanged using gamlss2_control. Additionally, if an optimizer is specified by the family object, this optimizer function will be employed for estimation.\n\n\nThe return value is determined by the object returned from the optimizer function, typically an object of class “gamlss2”. Default methods and extractor functions are available for this class. Nevertheless, users have the flexibility to supply their own optimizer function, along with user-specific methods tailored for the returned object.\n\n\n\n\n\nThe return value is determined by the object returned from the optimizer function. By default, the optimization is performed using the RS optimizer function (see gamlss2_control), yielding an object of class “gamlss2”. Default methods and extractor functions are available for this class.\n\n\n\nRigby RA, Stasinopoulos DM (2005). “Generalized Additive Models for Location, Scale and Shape (with Discussion).” Journal of the Royal Statistical Society, Series C (Applied Statistics), 54, 507–554. doi:10.1111/j.1467-9876.2005.00510.x\nRigby RA, Stasinopoulos DM, Heller GZ, De Bastiani F (2019). Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/9780429298547\nStasinopoulos DM, Rigby RA (2007). “Generalized Additive Models for Location Scale and Shape (GAMLSS) in R.” Journal of Statistical Software, 23(7), 1–46. doi:10.18637/jss.v023.i07\nStasinopoulos DM, Rigby RA, Heller GZ, Voudouris V, De Bastiani F (2017). Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/b21973\n\n\n\nRS, gamlss2_control, gamlss2.family\n\n\n\n\nlibrary(\"gamlss2\")\n\n\n## load the abdominal circumference data\ndata(\"abdom\", package = \"gamlss.data\")\n\n## specify the model Formula\nf <- y ~ s(x) | s(x) | s(x) | s(x)\n\n## estimate model\nb <- gamlss2(f, data = abdom, family = BCT)\n\nGAMLSS-RS iteration 1: Global Deviance = 4774.4683 eps = 0.534345 \nGAMLSS-RS iteration 2: Global Deviance = 4770.229 eps = 0.000887 \nGAMLSS-RS iteration 3: Global Deviance = 4770.1663 eps = 0.000013 \nGAMLSS-RS iteration 4: Global Deviance = 4770.1554 eps = 0.000002 \n\n## model summary\nsummary(b)\n\nCall:\ngamlss2(formula = f, data = abdom, family = BCT)\n---\nFamily: BCT \nLink function: mu = identity, sigma = log, nu = identity, tau = log\n*--------\nParameter: mu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 226.334 1.257 180 <2e-16 ***\n---\nSmooth terms:\n s(x)\nedf 4.551\n*--------\nParameter: sigma \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -2.92264 0.01101 -265.5 <2e-16 ***\n---\nSmooth terms:\n s(x)\nedf 2.5639\n*--------\nParameter: nu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -0.18021 0.04599 -3.918 9.95e-05 ***\n---\nSmooth terms:\n s(x)\nedf 1.0015\n*--------\nParameter: tau \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 2.6548 0.0144 184.4 <2e-16 ***\n---\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n---\nSmooth terms:\n s(x)\nedf 1.0042\n*--------\nn = 610 df = 13.12 res.df = 596.88\nDeviance = 4770.1554 Null Dev. Red. = 33.39%\nAIC = 4796.3966 elapsed = 0.78sec\n\n## plot estimated effects\nplot(b, which = \"effects\")\n\n\n\n\n\n\n\n## plot diagnostics\nplot(b, which = \"resid\")\n\n\n\n\n\n\n\n## predict parameters\npar <- predict(b)\n\n## predict quantiles\npq <- sapply(c(0.05, 0.5, 0.95), function(q) family(b)$q(q, par))\n\n## visualize\nplot(y ~ x, data = abdom, pch = 19,\n col = rgb(0.1, 0.1, 0.1, alpha = 0.3))\nmatplot(abdom$x, pq, type = \"l\", lwd = 2,\n lty = 1, col = 4, add = TRUE)\n\n\n\n\n\n\n\n## use of starting values\nm <- gamlss2(f, data = abdom, family = BCT,\n start = c(mu = 200, sigma = 0.1, nu = 0, tau = 10))\n\nGAMLSS-RS iteration 1: Global Deviance = 4789.7797 eps = 0.556012 \nGAMLSS-RS iteration 2: Global Deviance = 4774.5657 eps = 0.003176 \nGAMLSS-RS iteration 3: Global Deviance = 4771.4193 eps = 0.000658 \nGAMLSS-RS iteration 4: Global Deviance = 4769.9947 eps = 0.000298 \nGAMLSS-RS iteration 5: Global Deviance = 4769.9556 eps = 0.000008 \n\n## fix some parameters\nm <- gamlss2(f, data = abdom, family = BCT,\n start = c(mu = 200, sigma = 0.1, nu = 0, tau = 10),\n fixed = c(nu = TRUE, tau = TRUE))\n\nGAMLSS-RS iteration 1: Global Deviance = 4799.422 eps = 0.555118 \nGAMLSS-RS iteration 2: Global Deviance = 4795.2807 eps = 0.000862 \nGAMLSS-RS iteration 3: Global Deviance = 4795.2668 eps = 0.000002 \n\n## estimated coefficients (intercepts)\ncoef(m)\n\n mu.p.(Intercept) sigma.p.(Intercept) nu.p.(Intercept) tau.p.(Intercept) \n 226.347632 -2.922923 0.000000 2.302585 \n\n## starting values using full predictors\nm <- gamlss2(f, data = abdom, family = BCT,\n start = fitted(m))\n\nGAMLSS-RS iteration 1: Global Deviance = 4902.0767 eps = 0.372276 \nGAMLSS-RS iteration 2: Global Deviance = 4775.8465 eps = 0.025750 \nGAMLSS-RS iteration 3: Global Deviance = 4775.0302 eps = 0.000170 \nGAMLSS-RS iteration 4: Global Deviance = 4774.9582 eps = 0.000015 \nGAMLSS-RS iteration 5: Global Deviance = 4774.9519 eps = 0.000001 \n\n## same with\nm <- gamlss2(f, data = abdom, family = BCT,\n start = m)\n\nGAMLSS-RS iteration 1: Global Deviance = 4774.4683 eps = 0.534345 \nGAMLSS-RS iteration 2: Global Deviance = 4770.229 eps = 0.000887 \nGAMLSS-RS iteration 3: Global Deviance = 4770.1663 eps = 0.000013 \nGAMLSS-RS iteration 4: Global Deviance = 4770.1554 eps = 0.000002",
+ "text": "Estimation of generalized additive models for location scale and shape (GAMLSS). The model fitting function gamlss2() provides flexible infrastructures to estimate the parameters of a response distribution. The number of distributional parameters is not fixed, see gamlss2.family. Moreover, gamlss2() supports all smooth term constructors from the mgcv package in addition to the classical model terms as provided by gamlss and gamlss.add.\n\n\n\ngamlss2(x, ...)\n\n## S3 method for class 'formula'\ngamlss2(formula, data, family = NO,\n subset, na.action, weights, offset, start = NULL,\n control = gamlss2_control(...), ...)\n\n## S3 method for class 'list'\ngamlss2(x, ...)\n\n\n\n\n\n\n\nformula\n\n\nA GAM-type formula or Formula. All smooth terms of the mgcv package are supported, see also formula.gam.\n\n\n\n\nx\n\n\nFor gamlss.list() x is a list of formulas.\n\n\n\n\ndata\n\n\nA data frame or list or environment containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which gamlss2 is called.\n\n\n\n\nfamily\n\n\nA gamlss.family or gamlss2.family object used to define distribution and the link functions of the parameters.\n\n\n\n\nsubset\n\n\nAn optional vector specifying a subset of observations to be used in the fitting process.\n\n\n\n\nna.action\n\n\nNA processing for setting up the model.frame.\n\n\n\n\nweights\n\n\nAn optional vector of prior weights to be used in the fitting process. Should be NULL or a numeric vector.\n\n\n\n\noffset\n\n\nThis can be used to specify an a priori known components to be included in the linear predictors during fitting. Please note that if only a single numeric vector is provided, the offset will be assigned to the first specified parameter of the distribution. In the case of multiple offsets, a data frame or list must be supplied. Each offset is assigned in the same order as the parameters of the distribution specified in the family object.\n\n\n\n\nstart\n\n\nStarting values for estimation algorithms.\n\n\n\n\ncontrol\n\n\nA list of control arguments, see gamlss2_control.\n\n\n\n\n…\n\n\nArguments passed to gamlss2_control.\n\n\n\n\n\n\nThe model fitting function gamlss2() provides flexible infrastructures for the estimation of GAMLSS.\n\n\nDistributional models are specified using family objects, either from the gamlss.dist package or using gamlss2.family objects.\n\n\nEstimation is carried out through a Newton-Raphson/Fisher scoring algorithm, see function RS. The estimation algorithms can also be exchanged using gamlss2_control. Additionally, if an optimizer is specified by the family object, this optimizer function will be employed for estimation.\n\n\nThe return value is determined by the object returned from the optimizer function, typically an object of class “gamlss2”. Default methods and extractor functions are available for this class. Nevertheless, users have the flexibility to supply their own optimizer function, along with user-specific methods tailored for the returned object.\n\n\n\n\n\nThe return value is determined by the object returned from the optimizer function. By default, the optimization is performed using the RS optimizer function (see gamlss2_control), yielding an object of class “gamlss2”. Default methods and extractor functions are available for this class.\n\n\n\nRigby RA, Stasinopoulos DM (2005). “Generalized Additive Models for Location, Scale and Shape (with Discussion).” Journal of the Royal Statistical Society, Series C (Applied Statistics), 54, 507–554. doi:10.1111/j.1467-9876.2005.00510.x\nRigby RA, Stasinopoulos DM, Heller GZ, De Bastiani F (2019). Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/9780429298547\nStasinopoulos DM, Rigby RA (2007). “Generalized Additive Models for Location Scale and Shape (GAMLSS) in R.” Journal of Statistical Software, 23(7), 1–46. doi:10.18637/jss.v023.i07\nStasinopoulos DM, Rigby RA, Heller GZ, Voudouris V, De Bastiani F (2017). Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/b21973\n\n\n\nRS, gamlss2_control, gamlss2.family\n\n\n\n\nlibrary(\"gamlss2\")\n\n\n## load the abdominal circumference data\ndata(\"abdom\", package = \"gamlss.data\")\n\n## specify the model Formula\nf <- y ~ s(x) | s(x) | s(x) | s(x)\n\n## estimate model\nb <- gamlss2(f, data = abdom, family = BCT)\n\nGAMLSS-RS iteration 1: Global Deviance = 4774.4683 eps = 0.534345 \nGAMLSS-RS iteration 2: Global Deviance = 4770.229 eps = 0.000887 \nGAMLSS-RS iteration 3: Global Deviance = 4770.1663 eps = 0.000013 \nGAMLSS-RS iteration 4: Global Deviance = 4770.1554 eps = 0.000002 \n\n## model summary\nsummary(b)\n\nCall:\ngamlss2(formula = f, data = abdom, family = BCT)\n---\nFamily: BCT \nLink function: mu = identity, sigma = log, nu = identity, tau = log\n*--------\nParameter: mu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 226.334 1.257 180 <2e-16 ***\n---\nSmooth terms:\n s(x)\nedf 4.551\n*--------\nParameter: sigma \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -2.92264 0.01101 -265.5 <2e-16 ***\n---\nSmooth terms:\n s(x)\nedf 2.5639\n*--------\nParameter: nu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -0.18021 0.04599 -3.918 9.95e-05 ***\n---\nSmooth terms:\n s(x)\nedf 1.0015\n*--------\nParameter: tau \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 2.6548 0.0144 184.4 <2e-16 ***\n---\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n---\nSmooth terms:\n s(x)\nedf 1.0042\n*--------\nn = 610 df = 13.12 res.df = 596.88\nDeviance = 4770.1554 Null Dev. Red. = 33.39%\nAIC = 4796.3966 elapsed = 0.77sec\n\n## plot estimated effects\nplot(b, which = \"effects\")\n\n\n\n\n\n\n\n## plot diagnostics\nplot(b, which = \"resid\")\n\n\n\n\n\n\n\n## predict parameters\npar <- predict(b)\n\n## predict quantiles\npq <- sapply(c(0.05, 0.5, 0.95), function(q) family(b)$q(q, par))\n\n## visualize\nplot(y ~ x, data = abdom, pch = 19,\n col = rgb(0.1, 0.1, 0.1, alpha = 0.3))\nmatplot(abdom$x, pq, type = \"l\", lwd = 2,\n lty = 1, col = 4, add = TRUE)\n\n\n\n\n\n\n\n## use of starting values\nm <- gamlss2(f, data = abdom, family = BCT,\n start = c(mu = 200, sigma = 0.1, nu = 0, tau = 10))\n\nGAMLSS-RS iteration 1: Global Deviance = 4789.7797 eps = 0.556012 \nGAMLSS-RS iteration 2: Global Deviance = 4774.5657 eps = 0.003176 \nGAMLSS-RS iteration 3: Global Deviance = 4771.4193 eps = 0.000658 \nGAMLSS-RS iteration 4: Global Deviance = 4769.9947 eps = 0.000298 \nGAMLSS-RS iteration 5: Global Deviance = 4769.9556 eps = 0.000008 \n\n## fix some parameters\nm <- gamlss2(f, data = abdom, family = BCT,\n start = c(mu = 200, sigma = 0.1, nu = 0, tau = 10),\n fixed = c(nu = TRUE, tau = TRUE))\n\nGAMLSS-RS iteration 1: Global Deviance = 4799.422 eps = 0.555118 \nGAMLSS-RS iteration 2: Global Deviance = 4795.2807 eps = 0.000862 \nGAMLSS-RS iteration 3: Global Deviance = 4795.2668 eps = 0.000002 \n\n## estimated coefficients (intercepts)\ncoef(m)\n\n mu.p.(Intercept) sigma.p.(Intercept) nu.p.(Intercept) tau.p.(Intercept) \n 226.347632 -2.922923 0.000000 2.302585 \n\n## starting values using full predictors\nm <- gamlss2(f, data = abdom, family = BCT,\n start = fitted(m))\n\nGAMLSS-RS iteration 1: Global Deviance = 4902.0767 eps = 0.372276 \nGAMLSS-RS iteration 2: Global Deviance = 4775.8465 eps = 0.025750 \nGAMLSS-RS iteration 3: Global Deviance = 4775.0302 eps = 0.000170 \nGAMLSS-RS iteration 4: Global Deviance = 4774.9582 eps = 0.000015 \nGAMLSS-RS iteration 5: Global Deviance = 4774.9519 eps = 0.000001 \n\n## same with\nm <- gamlss2(f, data = abdom, family = BCT,\n start = m)\n\nGAMLSS-RS iteration 1: Global Deviance = 4774.4683 eps = 0.534345 \nGAMLSS-RS iteration 2: Global Deviance = 4770.229 eps = 0.000887 \nGAMLSS-RS iteration 3: Global Deviance = 4770.1663 eps = 0.000013 \nGAMLSS-RS iteration 4: Global Deviance = 4770.1554 eps = 0.000002",
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"title": "gamlss2",
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- "text": "Methods for gamlss2 model objects for extracting fitted (in-sample) or predicted (out-of-sample) probability distributions as distributions3 objects.\n\n\n\n## S3 method for class 'gamlss2'\nprodist(object, ...)\n\n\n\n\n\n\n\nobject\n\n\nA model object of class gamlss2.\n\n\n\n\n…\n\n\nArguments passed on to predict.gamlss2, e.g., newdata.\n\n\n\n\n\n\nTo facilitate making probabilistic forecasts based on gamlss2 model objects, the prodist method extracts fitted or predicted probability distribution objects. Internally, the predict.gamlss2 method is used first to obtain the distribution parameters (mu, sigma, tau, nu, or a subset thereof). Subsequently, the corresponding distribution object is set up using the GAMLSS class from the gamlss.dist package, enabling the workflow provided by the distributions3 package (see Zeileis et al. 2022).\nNote that these probability distributions only reflect the random variation in the dependent variable based on the model employed (and its associated distributional assumption for the dependent variable). This does not capture the uncertainty in the parameter estimates.\n\n\n\nAn object of class GAMLSS inheriting from distribution.\n\n\n\nZeileis A, Lang MN, Hayes A (2022). “distributions3: From Basic Probability to Probabilistic Regression.” Presented at useR! 2022 - The R User Conference. Slides, video, vignette, code at https://www.zeileis.org/news/user2022/.\n\n\n\nGAMLSS, predict.gamlss2\n\n\n\n\nlibrary(\"gamlss2\")\n\n\n## packages, code, and data\nlibrary(\"distributions3\")\ndata(\"cars\", package = \"datasets\")\n\n## fit heteroscedastic normal GAMLSS model\n## stopping distance (ft) explained by speed (mph)\nm <- gamlss2(dist ~ s(speed) | s(speed), data = cars, family = NO)\n\nGAMLSS-RS iteration 1: Global Deviance = 407.3541 eps = 0.125497 \nGAMLSS-RS iteration 2: Global Deviance = 405.7146 eps = 0.004024 \nGAMLSS-RS iteration 3: Global Deviance = 405.6978 eps = 0.000041 \nGAMLSS-RS iteration 4: Global Deviance = 405.6976 eps = 0.000000 \n\n## obtain predicted distributions for three levels of speed\nd <- prodist(m, newdata = data.frame(speed = c(10, 20, 30)))\nprint(d)\n\n 1 2 \n\"GAMLSS NO(mu = 23.04, sigma = 10.06)\" \"GAMLSS NO(mu = 59.04, sigma = 18.51)\" \n 3 \n\"GAMLSS NO(mu = 96.35, sigma = 33.95)\" \n\n## obtain quantiles (works the same for any distribution object 'd' !)\nquantile(d, 0.5)\n\n 1 2 3 \n23.03912 59.03607 96.34896 \n\nquantile(d, c(0.05, 0.5, 0.95), elementwise = FALSE)\n\n q_0.05 q_0.5 q_0.95\n1 6.486962 23.03912 39.59128\n2 28.589641 59.03607 89.48250\n3 40.504887 96.34896 152.19303\n\nquantile(d, c(0.05, 0.5, 0.95), elementwise = TRUE)\n\n 1 2 3 \n 6.486962 59.036073 152.193030 \n\n## visualization\nplot(dist ~ speed, data = cars)\nnd <- data.frame(speed = 0:240/4)\nnd$dist <- prodist(m, newdata = nd)\nnd$fit <- quantile(nd$dist, c(0.05, 0.5, 0.95))\nmatplot(nd$speed, nd$fit, type = \"l\", lty = 1, col = \"slategray\", add = TRUE)\n\n\n\n\n\n\n\n## moments\nmean(d)\n\n 1 2 3 \n23.03912 59.03607 96.34896 \n\nvariance(d)\n\n 1 2 3 \n 101.2639 342.6244 1152.6558 \n\n## simulate random numbers\nrandom(d, 5)\n\n r_1 r_2 r_3 r_4 r_5\n1 49.46417 43.74521 15.64832 16.14411 24.40045\n2 48.73735 39.49597 28.76521 60.20798 32.97853\n3 135.79246 117.37999 118.64879 92.26730 100.15979\n\n## density and distribution\npdf(d, 50 * -2:2)\n\n d_-100 d_-50 d_0 d_50 d_100\n1 1.365786e-34 1.440750e-13 0.0028836944 0.001095127 7.891037e-15\n2 2.012473e-18 6.289547e-10 0.0001332376 0.019131662 1.862073e-03\n3 6.414012e-10 1.084300e-06 0.0002095201 0.004627633 1.168286e-02\n\ncdf(d, 50 * -2:2)\n\n p_-100 p_-50 p_0 p_50 p_100\n1 1.116699e-34 1.961566e-13 0.0110254856 0.99631019 1.0000000\n2 4.279141e-18 1.923739e-09 0.0007128545 0.31271491 0.9865531\n3 3.661574e-09 8.139843e-06 0.0022705648 0.08609812 0.5428194\n\n## Poisson example\ndata(\"FIFA2018\", package = \"distributions3\")\nm2 <- gamlss2(goals ~ s(difference), data = FIFA2018, family = PO)\n\nGAMLSS-RS iteration 1: Global Deviance = 355.3922 eps = 0.045332 \nGAMLSS-RS iteration 2: Global Deviance = 355.3922 eps = 0.000000 \n\nd2 <- prodist(m2, newdata = data.frame(difference = 0))\nprint(d2)\n\n 1 \n\"GAMLSS PO(mu = 1.237)\" \n\nquantile(d2, c(0.05, 0.5, 0.95))\n\n[1] 0 1 3\n\n## note that log_pdf() can replicate logLik() value\nsum(log_pdf(prodist(m2), FIFA2018$goals))\n\n[1] -177.6961\n\nlogLik(m2)\n\n'log Lik.' -177.6961 (df=2.005144)",
+ "text": "Methods for gamlss2 model objects for extracting fitted (in-sample) or predicted (out-of-sample) probability distributions as distributions3 objects.\n\n\n\n## S3 method for class 'gamlss2'\nprodist(object, ...)\n\n\n\n\n\n\n\nobject\n\n\nA model object of class gamlss2.\n\n\n\n\n…\n\n\nArguments passed on to predict.gamlss2, e.g., newdata.\n\n\n\n\n\n\nTo facilitate making probabilistic forecasts based on gamlss2 model objects, the prodist method extracts fitted or predicted probability distribution objects. Internally, the predict.gamlss2 method is used first to obtain the distribution parameters (mu, sigma, tau, nu, or a subset thereof). Subsequently, the corresponding distribution object is set up using the GAMLSS class from the gamlss.dist package, enabling the workflow provided by the distributions3 package (see Zeileis et al. 2022).\nNote that these probability distributions only reflect the random variation in the dependent variable based on the model employed (and its associated distributional assumption for the dependent variable). This does not capture the uncertainty in the parameter estimates.\n\n\n\nAn object of class GAMLSS inheriting from distribution.\n\n\n\nZeileis A, Lang MN, Hayes A (2022). “distributions3: From Basic Probability to Probabilistic Regression.” Presented at useR! 2022 - The R User Conference. Slides, video, vignette, code at https://www.zeileis.org/news/user2022/.\n\n\n\nGAMLSS, predict.gamlss2\n\n\n\n\nlibrary(\"gamlss2\")\n\n\n## packages, code, and data\nlibrary(\"distributions3\")\ndata(\"cars\", package = \"datasets\")\n\n## fit heteroscedastic normal GAMLSS model\n## stopping distance (ft) explained by speed (mph)\nm <- gamlss2(dist ~ s(speed) | s(speed), data = cars, family = NO)\n\nGAMLSS-RS iteration 1: Global Deviance = 407.3541 eps = 0.125497 \nGAMLSS-RS iteration 2: Global Deviance = 405.7146 eps = 0.004024 \nGAMLSS-RS iteration 3: Global Deviance = 405.6978 eps = 0.000041 \nGAMLSS-RS iteration 4: Global Deviance = 405.6976 eps = 0.000000 \n\n## obtain predicted distributions for three levels of speed\nd <- prodist(m, newdata = data.frame(speed = c(10, 20, 30)))\nprint(d)\n\n 1 2 \n\"GAMLSS NO(mu = 23.04, sigma = 10.06)\" \"GAMLSS NO(mu = 59.04, sigma = 18.51)\" \n 3 \n\"GAMLSS NO(mu = 96.35, sigma = 33.95)\" \n\n## obtain quantiles (works the same for any distribution object 'd' !)\nquantile(d, 0.5)\n\n 1 2 3 \n23.03912 59.03607 96.34896 \n\nquantile(d, c(0.05, 0.5, 0.95), elementwise = FALSE)\n\n q_0.05 q_0.5 q_0.95\n1 6.486962 23.03912 39.59128\n2 28.589641 59.03607 89.48250\n3 40.504887 96.34896 152.19303\n\nquantile(d, c(0.05, 0.5, 0.95), elementwise = TRUE)\n\n 1 2 3 \n 6.486962 59.036073 152.193030 \n\n## visualization\nplot(dist ~ speed, data = cars)\nnd <- data.frame(speed = 0:240/4)\nnd$dist <- prodist(m, newdata = nd)\nnd$fit <- quantile(nd$dist, c(0.05, 0.5, 0.95))\nmatplot(nd$speed, nd$fit, type = \"l\", lty = 1, col = \"slategray\", add = TRUE)\n\n\n\n\n\n\n\n## moments\nmean(d)\n\n 1 2 3 \n23.03912 59.03607 96.34896 \n\nvariance(d)\n\n 1 2 3 \n 101.2639 342.6244 1152.6558 \n\n## simulate random numbers\nrandom(d, 5)\n\n r_1 r_2 r_3 r_4 r_5\n1 29.15083 28.25206 37.54823 22.39143 19.20124\n2 79.74554 43.36832 71.38394 32.39768 52.17705\n3 78.58056 169.09076 172.99766 106.80344 82.23454\n\n## density and distribution\npdf(d, 50 * -2:2)\n\n d_-100 d_-50 d_0 d_50 d_100\n1 1.365786e-34 1.440750e-13 0.0028836944 0.001095127 7.891037e-15\n2 2.012473e-18 6.289547e-10 0.0001332376 0.019131662 1.862073e-03\n3 6.414012e-10 1.084300e-06 0.0002095201 0.004627633 1.168286e-02\n\ncdf(d, 50 * -2:2)\n\n p_-100 p_-50 p_0 p_50 p_100\n1 1.116699e-34 1.961566e-13 0.0110254856 0.99631019 1.0000000\n2 4.279141e-18 1.923739e-09 0.0007128545 0.31271491 0.9865531\n3 3.661574e-09 8.139843e-06 0.0022705648 0.08609812 0.5428194\n\n## Poisson example\ndata(\"FIFA2018\", package = \"distributions3\")\nm2 <- gamlss2(goals ~ s(difference), data = FIFA2018, family = PO)\n\nGAMLSS-RS iteration 1: Global Deviance = 355.3922 eps = 0.045332 \nGAMLSS-RS iteration 2: Global Deviance = 355.3922 eps = 0.000000 \n\nd2 <- prodist(m2, newdata = data.frame(difference = 0))\nprint(d2)\n\n 1 \n\"GAMLSS PO(mu = 1.237)\" \n\nquantile(d2, c(0.05, 0.5, 0.95))\n\n[1] 0 1 3\n\n## note that log_pdf() can replicate logLik() value\nsum(log_pdf(prodist(m2), FIFA2018$goals))\n\n[1] -177.6961\n\nlogLik(m2)\n\n'log Lik.' -177.6961 (df=2.005144)",
"crumbs": [
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"prodist.gamlss2"
@@ -618,7 +618,7 @@
"href": "man/prodist.gamlss2.html#extracting-fitted-or-predicted-probability-distributions-from-gamlss2-models",
"title": "gamlss2",
"section": "",
- "text": "Methods for gamlss2 model objects for extracting fitted (in-sample) or predicted (out-of-sample) probability distributions as distributions3 objects.\n\n\n\n## S3 method for class 'gamlss2'\nprodist(object, ...)\n\n\n\n\n\n\n\nobject\n\n\nA model object of class gamlss2.\n\n\n\n\n…\n\n\nArguments passed on to predict.gamlss2, e.g., newdata.\n\n\n\n\n\n\nTo facilitate making probabilistic forecasts based on gamlss2 model objects, the prodist method extracts fitted or predicted probability distribution objects. Internally, the predict.gamlss2 method is used first to obtain the distribution parameters (mu, sigma, tau, nu, or a subset thereof). Subsequently, the corresponding distribution object is set up using the GAMLSS class from the gamlss.dist package, enabling the workflow provided by the distributions3 package (see Zeileis et al. 2022).\nNote that these probability distributions only reflect the random variation in the dependent variable based on the model employed (and its associated distributional assumption for the dependent variable). This does not capture the uncertainty in the parameter estimates.\n\n\n\nAn object of class GAMLSS inheriting from distribution.\n\n\n\nZeileis A, Lang MN, Hayes A (2022). “distributions3: From Basic Probability to Probabilistic Regression.” Presented at useR! 2022 - The R User Conference. Slides, video, vignette, code at https://www.zeileis.org/news/user2022/.\n\n\n\nGAMLSS, predict.gamlss2\n\n\n\n\nlibrary(\"gamlss2\")\n\n\n## packages, code, and data\nlibrary(\"distributions3\")\ndata(\"cars\", package = \"datasets\")\n\n## fit heteroscedastic normal GAMLSS model\n## stopping distance (ft) explained by speed (mph)\nm <- gamlss2(dist ~ s(speed) | s(speed), data = cars, family = NO)\n\nGAMLSS-RS iteration 1: Global Deviance = 407.3541 eps = 0.125497 \nGAMLSS-RS iteration 2: Global Deviance = 405.7146 eps = 0.004024 \nGAMLSS-RS iteration 3: Global Deviance = 405.6978 eps = 0.000041 \nGAMLSS-RS iteration 4: Global Deviance = 405.6976 eps = 0.000000 \n\n## obtain predicted distributions for three levels of speed\nd <- prodist(m, newdata = data.frame(speed = c(10, 20, 30)))\nprint(d)\n\n 1 2 \n\"GAMLSS NO(mu = 23.04, sigma = 10.06)\" \"GAMLSS NO(mu = 59.04, sigma = 18.51)\" \n 3 \n\"GAMLSS NO(mu = 96.35, sigma = 33.95)\" \n\n## obtain quantiles (works the same for any distribution object 'd' !)\nquantile(d, 0.5)\n\n 1 2 3 \n23.03912 59.03607 96.34896 \n\nquantile(d, c(0.05, 0.5, 0.95), elementwise = FALSE)\n\n q_0.05 q_0.5 q_0.95\n1 6.486962 23.03912 39.59128\n2 28.589641 59.03607 89.48250\n3 40.504887 96.34896 152.19303\n\nquantile(d, c(0.05, 0.5, 0.95), elementwise = TRUE)\n\n 1 2 3 \n 6.486962 59.036073 152.193030 \n\n## visualization\nplot(dist ~ speed, data = cars)\nnd <- data.frame(speed = 0:240/4)\nnd$dist <- prodist(m, newdata = nd)\nnd$fit <- quantile(nd$dist, c(0.05, 0.5, 0.95))\nmatplot(nd$speed, nd$fit, type = \"l\", lty = 1, col = \"slategray\", add = TRUE)\n\n\n\n\n\n\n\n## moments\nmean(d)\n\n 1 2 3 \n23.03912 59.03607 96.34896 \n\nvariance(d)\n\n 1 2 3 \n 101.2639 342.6244 1152.6558 \n\n## simulate random numbers\nrandom(d, 5)\n\n r_1 r_2 r_3 r_4 r_5\n1 49.46417 43.74521 15.64832 16.14411 24.40045\n2 48.73735 39.49597 28.76521 60.20798 32.97853\n3 135.79246 117.37999 118.64879 92.26730 100.15979\n\n## density and distribution\npdf(d, 50 * -2:2)\n\n d_-100 d_-50 d_0 d_50 d_100\n1 1.365786e-34 1.440750e-13 0.0028836944 0.001095127 7.891037e-15\n2 2.012473e-18 6.289547e-10 0.0001332376 0.019131662 1.862073e-03\n3 6.414012e-10 1.084300e-06 0.0002095201 0.004627633 1.168286e-02\n\ncdf(d, 50 * -2:2)\n\n p_-100 p_-50 p_0 p_50 p_100\n1 1.116699e-34 1.961566e-13 0.0110254856 0.99631019 1.0000000\n2 4.279141e-18 1.923739e-09 0.0007128545 0.31271491 0.9865531\n3 3.661574e-09 8.139843e-06 0.0022705648 0.08609812 0.5428194\n\n## Poisson example\ndata(\"FIFA2018\", package = \"distributions3\")\nm2 <- gamlss2(goals ~ s(difference), data = FIFA2018, family = PO)\n\nGAMLSS-RS iteration 1: Global Deviance = 355.3922 eps = 0.045332 \nGAMLSS-RS iteration 2: Global Deviance = 355.3922 eps = 0.000000 \n\nd2 <- prodist(m2, newdata = data.frame(difference = 0))\nprint(d2)\n\n 1 \n\"GAMLSS PO(mu = 1.237)\" \n\nquantile(d2, c(0.05, 0.5, 0.95))\n\n[1] 0 1 3\n\n## note that log_pdf() can replicate logLik() value\nsum(log_pdf(prodist(m2), FIFA2018$goals))\n\n[1] -177.6961\n\nlogLik(m2)\n\n'log Lik.' -177.6961 (df=2.005144)",
+ "text": "Methods for gamlss2 model objects for extracting fitted (in-sample) or predicted (out-of-sample) probability distributions as distributions3 objects.\n\n\n\n## S3 method for class 'gamlss2'\nprodist(object, ...)\n\n\n\n\n\n\n\nobject\n\n\nA model object of class gamlss2.\n\n\n\n\n…\n\n\nArguments passed on to predict.gamlss2, e.g., newdata.\n\n\n\n\n\n\nTo facilitate making probabilistic forecasts based on gamlss2 model objects, the prodist method extracts fitted or predicted probability distribution objects. Internally, the predict.gamlss2 method is used first to obtain the distribution parameters (mu, sigma, tau, nu, or a subset thereof). Subsequently, the corresponding distribution object is set up using the GAMLSS class from the gamlss.dist package, enabling the workflow provided by the distributions3 package (see Zeileis et al. 2022).\nNote that these probability distributions only reflect the random variation in the dependent variable based on the model employed (and its associated distributional assumption for the dependent variable). This does not capture the uncertainty in the parameter estimates.\n\n\n\nAn object of class GAMLSS inheriting from distribution.\n\n\n\nZeileis A, Lang MN, Hayes A (2022). “distributions3: From Basic Probability to Probabilistic Regression.” Presented at useR! 2022 - The R User Conference. Slides, video, vignette, code at https://www.zeileis.org/news/user2022/.\n\n\n\nGAMLSS, predict.gamlss2\n\n\n\n\nlibrary(\"gamlss2\")\n\n\n## packages, code, and data\nlibrary(\"distributions3\")\ndata(\"cars\", package = \"datasets\")\n\n## fit heteroscedastic normal GAMLSS model\n## stopping distance (ft) explained by speed (mph)\nm <- gamlss2(dist ~ s(speed) | s(speed), data = cars, family = NO)\n\nGAMLSS-RS iteration 1: Global Deviance = 407.3541 eps = 0.125497 \nGAMLSS-RS iteration 2: Global Deviance = 405.7146 eps = 0.004024 \nGAMLSS-RS iteration 3: Global Deviance = 405.6978 eps = 0.000041 \nGAMLSS-RS iteration 4: Global Deviance = 405.6976 eps = 0.000000 \n\n## obtain predicted distributions for three levels of speed\nd <- prodist(m, newdata = data.frame(speed = c(10, 20, 30)))\nprint(d)\n\n 1 2 \n\"GAMLSS NO(mu = 23.04, sigma = 10.06)\" \"GAMLSS NO(mu = 59.04, sigma = 18.51)\" \n 3 \n\"GAMLSS NO(mu = 96.35, sigma = 33.95)\" \n\n## obtain quantiles (works the same for any distribution object 'd' !)\nquantile(d, 0.5)\n\n 1 2 3 \n23.03912 59.03607 96.34896 \n\nquantile(d, c(0.05, 0.5, 0.95), elementwise = FALSE)\n\n q_0.05 q_0.5 q_0.95\n1 6.486962 23.03912 39.59128\n2 28.589641 59.03607 89.48250\n3 40.504887 96.34896 152.19303\n\nquantile(d, c(0.05, 0.5, 0.95), elementwise = TRUE)\n\n 1 2 3 \n 6.486962 59.036073 152.193030 \n\n## visualization\nplot(dist ~ speed, data = cars)\nnd <- data.frame(speed = 0:240/4)\nnd$dist <- prodist(m, newdata = nd)\nnd$fit <- quantile(nd$dist, c(0.05, 0.5, 0.95))\nmatplot(nd$speed, nd$fit, type = \"l\", lty = 1, col = \"slategray\", add = TRUE)\n\n\n\n\n\n\n\n## moments\nmean(d)\n\n 1 2 3 \n23.03912 59.03607 96.34896 \n\nvariance(d)\n\n 1 2 3 \n 101.2639 342.6244 1152.6558 \n\n## simulate random numbers\nrandom(d, 5)\n\n r_1 r_2 r_3 r_4 r_5\n1 29.15083 28.25206 37.54823 22.39143 19.20124\n2 79.74554 43.36832 71.38394 32.39768 52.17705\n3 78.58056 169.09076 172.99766 106.80344 82.23454\n\n## density and distribution\npdf(d, 50 * -2:2)\n\n d_-100 d_-50 d_0 d_50 d_100\n1 1.365786e-34 1.440750e-13 0.0028836944 0.001095127 7.891037e-15\n2 2.012473e-18 6.289547e-10 0.0001332376 0.019131662 1.862073e-03\n3 6.414012e-10 1.084300e-06 0.0002095201 0.004627633 1.168286e-02\n\ncdf(d, 50 * -2:2)\n\n p_-100 p_-50 p_0 p_50 p_100\n1 1.116699e-34 1.961566e-13 0.0110254856 0.99631019 1.0000000\n2 4.279141e-18 1.923739e-09 0.0007128545 0.31271491 0.9865531\n3 3.661574e-09 8.139843e-06 0.0022705648 0.08609812 0.5428194\n\n## Poisson example\ndata(\"FIFA2018\", package = \"distributions3\")\nm2 <- gamlss2(goals ~ s(difference), data = FIFA2018, family = PO)\n\nGAMLSS-RS iteration 1: Global Deviance = 355.3922 eps = 0.045332 \nGAMLSS-RS iteration 2: Global Deviance = 355.3922 eps = 0.000000 \n\nd2 <- prodist(m2, newdata = data.frame(difference = 0))\nprint(d2)\n\n 1 \n\"GAMLSS PO(mu = 1.237)\" \n\nquantile(d2, c(0.05, 0.5, 0.95))\n\n[1] 0 1 3\n\n## note that log_pdf() can replicate logLik() value\nsum(log_pdf(prodist(m2), FIFA2018$goals))\n\n[1] -177.6961\n\nlogLik(m2)\n\n'log Lik.' -177.6961 (df=2.005144)",
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@@ -804,7 +804,7 @@
"href": "vignettes/topmodels.html#probabilistic-model-infrastructure",
"title": "Forecasting and Assessment with topmodels",
"section": "1 Probabilistic model infrastructure",
- "text": "1 Probabilistic model infrastructure\nIntroduction on how to use the topmodels package (Zeileis, Lang, and Stauffer 2024) with gamlss2.\nCurrently not on CRAN, yet, so install from R-universe (if not done already). The development version of gamlss.dist is also needed.\n\nif(!(\"topmodels\" %in% installed.packages())) {\n install.packages(\"topmodels\", repos = \"https://zeileis.R-universe.dev\")\n}\nif(packageVersion(\"gamlss.dist\") < \"6.1-3\") {\n install.packages(\"gamlss.dist\", repos = \"https://gamlss-dev.R-universe.dev\")\n}\n\nOn GitHub, unfortunately, in the GitHub Action the gamlss.dist package is always taken from CRAN (via r-cran-gamlss.dist apparently).\n\npackageVersion(\"gamlss.dist\")\n\n[1] '6.1.1'\n\ngamlss_dist_devel <- packageVersion(\"gamlss.dist\") >= \"6.1-3\"",
+ "text": "1 Probabilistic model infrastructure\nIntroduction on how to use the topmodels package (topmodels?) with gamlss2.\nCurrently not on CRAN, yet, so install from R-universe (if not done already). The development version of gamlss.dist is also needed.\n\nif(!(\"topmodels\" %in% installed.packages())) {\n install.packages(\"topmodels\", repos = \"https://zeileis.R-universe.dev\")\n}\nif(packageVersion(\"gamlss.dist\") < \"6.1-3\") {\n install.packages(\"gamlss.dist\", repos = \"https://gamlss-dev.R-universe.dev\")\n}\n\nOn GitHub, unfortunately, in the GitHub Action the gamlss.dist package is always taken from CRAN (via r-cran-gamlss.dist apparently).\n\npackageVersion(\"gamlss.dist\")\n\n[1] '6.1.1'\n\ngamlss_dist_devel <- packageVersion(\"gamlss.dist\") >= \"6.1-3\"",
"crumbs": [
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"Forecasting and Assessment with topmodels"
@@ -925,7 +925,7 @@
"href": "vignettes/families.html",
"title": "Family Objects",
"section": "",
- "text": "Note that all family objects of the gamlss.dist package can be used for modeling. However, for users wanting to specify their own (new) distribution model, this document provides a guide on how to define custom family objects within the gamlss2 framework.\nFamily objects in the gamlss2 package play an essential role in defining the models used for fitting data to distributions. These objects encapsulate the necessary details about the distribution and the parameters, such as:\nThis document provides an overview of how to construct and use family objects within gamlss2. By the end, you should have a good understanding of how to implement a custom family for use in statistical models.",
+ "text": "All family objects of the gamlss.dist package, see Rigby et al. (2019), can be used for modelling in gamlss2. However, for users wanting to specify their own (new) distribution model, this document provides a guide on how to define custom family objects within the gamlss2 framework.\nFamily objects in the gamlss2 package play an essential role in defining the models used for fitting data to distributions. These objects encapsulate the necessary details about the distribution and the parameters, such as:\nThis document provides an overview of how to construct and use family objects within gamlss2. By the end, you should have a good understanding of how to implement a custom family for use in statistical models.",
"crumbs": [
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@@ -980,7 +980,7 @@
"href": "vignettes/families.html#flexible-links",
"title": "Family Objects",
"section": "5 Flexible Links",
- "text": "5 Flexible Links\nNote that the example above used static link functions to define the family object. However, users can easily create families with flexible link functions as well. A helpful example of how to implement such flexibility can be found in the Kumaraswamy distribution implementation, which provides a clear template for setting up families with customizable link functions.\nThe Kumaraswamy distribution is a continuous distribution defined on the interval \\((0, 1)\\). It is similar to the Beta distribution but has simpler forms for its cumulative distribution and inverse cumulative distribution functions, making it more computationally efficient for certain applications.\nThe probability density function (PDF) of the Kumaraswamy distribution is:\n\\[\nf(y; a, b) = aby^{a-1}(1 - y^a)^{b-1}\n\\]\nwhere \\(y \\in (0, 1)\\) is the response, and \\(a\\) and \\(b\\) are non-negative parameters that determine the shape of the distribution. The complete implementation, including flexible link functions is provided in the Kumaraswamy() family.\nIn the following example, we will create the family object for the Kumaraswamy distribution using the Kumaraswamy() function and estimate a model using this distribution.\n\n5.1 Example: Modeling with the Kumaraswamy Distribution\nIn this example, we will:\n\nDefine the Kumaraswamy family object.\nSimulate data based on this distribution.\nEstimate the model and plot the results.\n\n\n## Define the Kumaraswamy family object with specific link functions.\nfam <- Kumaraswamy(a.link = shiftlog, b.link = \"log\")\n\n## Set seed for reproducibility.\nset.seed(123)\n\n## Simulate data for 1000 observations.\nn <- 1000\nd <- data.frame(\"x\" = runif(n, -pi, pi))\n\n## Specify the true parameters.\npar <- data.frame(\n \"a\" = exp(1.2 + sin(d$x)) + 1, # Parameter 'a' depends on 'x'\n \"b\" = 1 # Parameter 'b' is constant\n)\n\n## Sample response values using the family object.\nd$y <- fam$r(1, par)\n\n## Estimate a model using the Kumaraswamy family.\nb <- gamlss2(y ~ s(x), data = d, family = fam)\n\nGAMLSS-RS iteration 1: Global Deviance = -1503.9982 eps = 0.674665 \nGAMLSS-RS iteration 2: Global Deviance = -1504.1075 eps = 0.000072 \nGAMLSS-RS iteration 3: Global Deviance = -1504.1262 eps = 0.000012 \nGAMLSS-RS iteration 4: Global Deviance = -1504.1294 eps = 0.000002 \n\n## Plot the estimated effect.\nplot(b)\n\n\n\n\n\n\n\n## Plot residual diagnostics.\nplot(b, which = \"resid\")\n\n\n\n\n\n\n\n\nIn this example, we simulated a dataset where the parameter a of the Kumaraswamy distribution varies with x following a sinusoidal pattern. We then used the gamlss2() function to fit a smooth model that estimates this relationship. The effect of x on y is plotted, followed by a diagnostic plot to assess residuals.\nThe Kumaraswamy() family in gamlss2 is flexible, allowing the user to specify different link functions for its parameters, such as the default shiftlog link function for parameter a, which ensures non-negative values.",
+ "text": "5 Flexible Links\nNote that the example above used static link functions to define the family object. However, users can easily create families with flexible link functions as well. A helpful example of how to implement such flexibility can be found in the Kumaraswamy distribution implementation, which provides a clear template for setting up families with customizable link functions.\nThe Kumaraswamy distribution is a continuous distribution defined on the interval \\((0, 1)\\). It is similar to the Beta distribution but has simpler forms for its cumulative distribution and inverse cumulative distribution functions, making it more computationally efficient for certain applications. Unfortunately the Kumaraswamy distribution parameters do not conform with the distribution regression principal that parameters should have a clear interpretation in terms of location and scale. For example, the mean and variance of the distribution are a rather complicated functions of the parameters a and b, nevertheless the distribution is a good example of two parameter distribution in which the parameters are not named as mu and sigma as in all distributions defined in Rigby et al. (2019).\nThe probability density function (PDF) of the Kumaraswamy distribution is:\n\\[\nf(y; a, b) = aby^{a-1}(1 - y^a)^{b-1}\n\\]\nwhere \\(y \\in (0, 1)\\) is the response, and \\(a\\) and \\(b\\) are non-negative parameters that determine the shape of the distribution. The complete implementation, including flexible link functions is provided in the Kumaraswamy() family.\nIn the following example, we will create the family object for the Kumaraswamy distribution using the Kumaraswamy() function and estimate a model using this distribution.\n\n5.1 Example: Modeling with the Kumaraswamy Distribution\nIn this example, we will:\n\nDefine the Kumaraswamy family object.\nSimulate data based on this distribution.\nEstimate the model and plot the results.\n\n\n## Define the Kumaraswamy family object with specific link functions.\nfam <- Kumaraswamy(a.link = shiftlog, b.link = \"log\")\n\n## Set seed for reproducibility.\nset.seed(123)\n\n## Simulate data for 1000 observations.\nn <- 1000\nd <- data.frame(\"x\" = runif(n, -pi, pi))\n\n## Specify the true parameters.\npar <- data.frame(\n \"a\" = exp(1.2 + sin(d$x)) + 1, # Parameter 'a' depends on 'x'\n \"b\" = 1 # Parameter 'b' is constant\n)\n\n## Sample response values using the family object.\nd$y <- fam$r(1, par)\n\n## Estimate a model using the Kumaraswamy family.\nb <- gamlss2(y ~ s(x), data = d, family = fam)\n\nGAMLSS-RS iteration 1: Global Deviance = -1503.9982 eps = 0.674665 \nGAMLSS-RS iteration 2: Global Deviance = -1504.1075 eps = 0.000072 \nGAMLSS-RS iteration 3: Global Deviance = -1504.1262 eps = 0.000012 \nGAMLSS-RS iteration 4: Global Deviance = -1504.1294 eps = 0.000002 \n\n## Plot the estimated effect.\nplot(b)\n\n\n\n\n\n\n\n## Plot residual diagnostics.\nplot(b, which = \"resid\")\n\n\n\n\n\n\n\n\nIn this example, we simulated a dataset where the parameter a of the Kumaraswamy distribution varies with x following a sinusoidal pattern. We then used the gamlss2() function to fit a smooth model that estimates this relationship. The effect of x on y is plotted, followed by a diagnostic plot to assess residuals.\nThe Kumaraswamy() family in gamlss2 is flexible, allowing the user to specify different link functions for its parameters, such as the default shiftlog link function for parameter a, which ensures non-negative values.",
"crumbs": [
"Articles",
"Family Objects"
diff --git a/vignettes/families.html b/vignettes/families.html
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--- a/vignettes/families.html
+++ b/vignettes/families.html
@@ -464,22 +464,22 @@
Family Objects
-
Note that all family objects of the gamlss.dist package can be used for modeling. However, for users wanting to specify their own (new) distribution model, this document provides a guide on how to define custom family objects within the gamlss2 framework.
-
Family objects in the gamlss2 package play an essential role in defining the models used for fitting data to distributions. These objects encapsulate the necessary details about the distribution and the parameters, such as:
+
All family objects of the gamlss.dist package, see Rigby et al. (2019), can be used for modelling in gamlss2. However, for users wanting to specify their own (new) distribution model, this document provides a guide on how to define custom family objects within the gamlss2 framework.
+
Family objects in the gamlss2 package play an essential role in defining the models used for fitting data to distributions. These objects encapsulate the necessary details about the distribution and the parameters, such as:
The names of the parameters.
The link functions that map the parameters to the predictor.
Functions for the density, log-likelihood, and their derivatives.
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This document provides an overview of how to construct and use family objects within gamlss2. By the end, you should have a good understanding of how to implement a custom family for use in statistical models.
+
This document provides an overview of how to construct and use family objects within gamlss2. By the end, you should have a good understanding of how to implement a custom family for use in statistical models.
1 Defining Family Objects
A family object in gamlss2 is a list that must meet the following minimum criteria:
-
Family Name: The object must contain the family name as a character string.
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Parameters: The object must list the parameters of the distribution (e.g., "mu" and "sigma" for a normal distribution).
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Link Functions: It must specify the link functions associated with each parameter.
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Density Function: A d() function must be provided to evaluate the (log-)density of the distribution.
+
Family Name: The object must contain the family name as a character string.
+
Parameters: The object must list the parameters of the distribution (e.g., "mu" and "sigma" for a normal distribution).
+
Link Functions: It must specify the link functions associated with each parameter.
+
Density Function: A d() function must be provided to evaluate the (log-)density of the distribution.
Optionally, a family object can include functions to calculate the log-likelihood, random number generation, cumulative distribution function (CDF), and quantile function.
Here’s an example of a minimal family object for the normal distribution.
@@ -566,7 +566,7 @@
5 Flexible Links
Note that the example above used static link functions to define the family object. However, users can easily create families with flexible link functions as well. A helpful example of how to implement such flexibility can be found in the Kumaraswamy distribution implementation, which provides a clear template for setting up families with customizable link functions.
-
The Kumaraswamy distribution is a continuous distribution defined on the interval \((0, 1)\). It is similar to the Beta distribution but has simpler forms for its cumulative distribution and inverse cumulative distribution functions, making it more computationally efficient for certain applications.
+
The Kumaraswamy distribution is a continuous distribution defined on the interval \((0, 1)\). It is similar to the Beta distribution but has simpler forms for its cumulative distribution and inverse cumulative distribution functions, making it more computationally efficient for certain applications. Unfortunately the Kumaraswamy distribution parameters do not conform with the distribution regression principal that parameters should have a clear interpretation in terms of location and scale. For example, the mean and variance of the distribution are a rather complicated functions of the parameters a and b, nevertheless the distribution is a good example of two parameter distribution in which the parameters are not named as mu and sigma as in all distributions defined in Rigby et al. (2019).
The probability density function (PDF) of the Kumaraswamy distribution is:
\[
f(y; a, b) = aby^{a-1}(1 - y^a)^{b-1}
@@ -644,6 +644,9 @@
Rigby, R. A., and D. M. Stasinopoulos. 2005. “Generalized Additive Models for Location, Scale and Shape.”Journal of the Royal Statistical Society C 54 (3): 507–54. https://doi.org/10.1111/j.1467-9876.2005.00510.x.
+
+Rigby, R. A., D. M. Stasinopoulos, G. Z. Heller, and F. De Bastiani. 2019. Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R. Boca Raton: Chapman & Hall/CRC. https://doi.org/10.1201/9780429298547.
+
