Title:	Generalized Additive Latent and Mixed Models
Version:	0.2.3
Description:	Estimates generalized additive latent and mixed models using maximum marginal likelihood, as defined in Sorensen et al. (2023) <doi:10.1007/s11336-023-09910-z>, which is an extension of Rabe-Hesketh and Skrondal (2004)'s unifying framework for multilevel latent variable modeling <doi:10.1007/BF02295939>. Efficient computation is done using sparse matrix methods, Laplace approximation, and automatic differentiation. The framework includes generalized multilevel models with heteroscedastic residuals, mixed response types, factor loadings, smoothing splines, crossed random effects, and combinations thereof. Syntax for model formulation is close to 'lme4' (Bates et al. (2015) <doi:10.18637/jss.v067.i01>) and 'PLmixed' (Rockwood and Jeon (2019) <doi:10.1080/00273171.2018.1516541>).
License:	GPL (≥ 3)
URL:	https://github.com/LCBC-UiO/galamm, https://lcbc-uio.github.io/galamm/
BugReports:	https://github.com/LCBC-UiO/galamm/issues
Encoding:	UTF-8
Imports:	lme4, Matrix, memoise, methods, mgcv, nlme, Rcpp, Rdpack, stats
Depends:	R (≥ 3.5.0)
LinkingTo:	Rcpp, RcppEigen
LazyData:	true
RoxygenNote:	7.3.2
Suggests:	covr, gamm4, knitr, PLmixed, rmarkdown, testthat (≥ 3.0.0)
Config/testthat/edition:	3
VignetteBuilder:	knitr, rmarkdown
RdMacros:	Rdpack
NeedsCompilation:	yes
SystemRequirements:	C++17
Packaged:	2025-07-03 13:46:01 UTC; oyss
Author:	Øystein Sørensen [aut, cre], Douglas Bates [ctb], Ben Bolker [ctb], Martin Maechler [ctb], Allan Leal [ctb], Fabian Scheipl [ctb], Steven Walker [ctb], Simon Wood [ctb]
Maintainer:	Øystein Sørensen <oystein.sorensen@psykologi.uio.no>
Repository:	CRAN
Date/Publication:	2025-07-03 14:00:02 UTC

galamm: Generalized Additive Latent and Mixed Models

Description

Estimates generalized additive latent and mixed models using maximum marginal likelihood, as defined in Sorensen et al. (2023) doi:10.1007/s11336-023-09910-z, which is an extension of Rabe-Hesketh and Skrondal (2004)'s unifying framework for multilevel latent variable modeling doi:10.1007/BF02295939. Efficient computation is done using sparse matrix methods, Laplace approximation, and automatic differentiation. The framework includes generalized multilevel models with heteroscedastic residuals, mixed response types, factor loadings, smoothing splines, crossed random effects, and combinations thereof. Syntax for model formulation is close to 'lme4' (Bates et al. (2015) doi:10.18637/jss.v067.i01) and 'PLmixed' (Rockwood and Jeon (2019) doi:10.1080/00273171.2018.1516541).

Author(s)

Maintainer: Øystein Sørensen oystein.sorensen@psykologi.uio.no (ORCID)

Other contributors:

• Douglas Bates [contributor]

• Ben Bolker [contributor]

• Martin Maechler [contributor]

• Allan Leal [contributor]

• Fabian Scheipl [contributor]

• Steven Walker [contributor]

• Simon Wood [contributor]

References

Sørensen Ø, Fjell AM, Walhovd KB (2023). “Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models.” Psychometrika, 88(2), 456–486. ISSN 1860-0980, doi:10.1007/s11336-023-09910-z.

See Also

Useful links:

• https://github.com/LCBC-UiO/galamm

• https://lcbc-uio.github.io/galamm/

• Report bugs at https://github.com/LCBC-UiO/galamm/issues

Extract variance and correlation components from model

Description

Extract variance and correlation components from model

Usage

## S3 method for class 'galamm'
VarCorr(x, sigma = 1, ...)

Arguments

Value

An object of class c("VarCorr.galamm", "VarCorr.merMod").

See Also

print.VarCorr.galamm() for the print function.

Other details of model fit: coef.galamm(), confint.galamm(), deviance.galamm(), factor_loadings.galamm(), family.galamm(), fitted.galamm(), fixef(), formula.galamm(), llikAIC(), logLik.galamm(), nobs.galamm(), predict.galamm(), print.VarCorr.galamm(), ranef.galamm(), residuals.galamm(), response(), sigma.galamm(), vcov.galamm()

Examples

# Linear mixed model with heteroscedastic residuals
mod <- galamm(
  formula = y ~ x + (1 | id),
  weights = ~ (1 | item),
  data = hsced
)

# Extract information on variance and covariance
VarCorr(mod)

# Convert to data frame
# (this invokes lme4's function as.data.frame.VarCorr.merMod)
as.data.frame(VarCorr(mod))

Compare likelihoods of galamm objects

Description

Anova function for comparing different GALAMMs fitted on the same data.

Usage

## S3 method for class 'galamm'
anova(object, ...)

Arguments

Value

A table with model comparison metric.

Author(s)

Some of the source code for this function is adapted from lme4:::anova.merMod, with authors Douglas M. Bates, Martin Maechler, Ben Bolker, and Steve Walker.

References

Bates DM, Mächler M, Bolker B, Walker S (2015). “Fitting Linear Mixed-Effects Models Using Lme4.” Journal of Statistical Software, 67(1), 1–48. ISSN 1548-7660, doi:10.18637/jss.v067.i01.

See Also

summary.galamm() for the summary method and anova() for the generic function.

Other summary functions: plot.galamm(), plot_smooth.galamm(), print.galamm(), print.summary.galamm(), summary.galamm()

Examples

# Poisson GLMM
count_mod <- galamm(
  formula = y ~ lbas * treat + lage + v4 + (1 | subj),
  data = epilep, family = poisson
)

# Model without interaction
count_mod0 <- galamm(
  formula = y ~ lbas + treat + lage + v4 + (1 | subj),
  data = epilep, family = poisson
)

# Model comparison
anova(count_mod, count_mod0)

Extract galamm coefficients

Description

Currently, this function only returns the fixed effects.

Usage

## S3 method for class 'galamm'
coef(object, ...)

Arguments

Value

A matrix with the requested coefficients.

See Also

fixef.galamm() for fixed effects, ranef.galamm() for random effects, and coef() for the generic function.

Other details of model fit: VarCorr(), confint.galamm(), deviance.galamm(), factor_loadings.galamm(), family.galamm(), fitted.galamm(), fixef(), formula.galamm(), llikAIC(), logLik.galamm(), nobs.galamm(), predict.galamm(), print.VarCorr.galamm(), ranef.galamm(), residuals.galamm(), response(), sigma.galamm(), vcov.galamm()

Examples

# Poisson GLMM
count_mod <- galamm(
  formula = y ~ lbas * treat + lage + v4 + (1 | subj),
  data = epilep, family = poisson
)

# Extract coefficients
coef(count_mod)

Simulated Data with Measurements of Cognitive Abilities

Description

Simulated dataset mimicking the measurement of abilities in three cognitive domains. The latent traits (cognitive ability in a given domain) are based on the functions in mgcv::gamSim (Wood 2017), and depend on the explanatory variable x.

Usage

cognition

Format

cognition A data frame with 14400 rows and 7 columns:

id

Subject ID.

domain

Factor variable denoting the cognitive domain.

x

Explanatory variable.

timepoint

Factor variable denoting the timepoint.

item

Factor variable denoting the item within the tests of each cognitive domain.

trials

Number of trials, if applicable.

y

Response variable. For domain 1 a real number, for domain 2 a binomially distributed variable based on a single trial, for domain 3 a real number.

References

Wood SN (2017). Generalized Additive Models: An Introduction with R, 2 edition. Chapman and Hall/CRC.

See Also

Other datasets: diet, epilep, hsced, latent_covariates, latent_covariates_long, lifespan, mresp, mresp_hsced

Confidence intervals for model parameters

Description

Confidence intervals for model parameters

Usage

## S3 method for class 'galamm'
confint(object, parm, level = 0.95, method = "Wald", ...)

Arguments

Value

A matrix with the requested confidence intervals.

See Also

fixef.galamm() for fixed effects, coef.galamm() for coefficients more generally, and vcov.galamm() for the variance-covariance matrix. confint() is the generic function.

Other details of model fit: VarCorr(), coef.galamm(), deviance.galamm(), factor_loadings.galamm(), family.galamm(), fitted.galamm(), fixef(), formula.galamm(), llikAIC(), logLik.galamm(), nobs.galamm(), predict.galamm(), print.VarCorr.galamm(), ranef.galamm(), residuals.galamm(), response(), sigma.galamm(), vcov.galamm()

Examples

# Poisson GLMM
count_mod <- galamm(
  formula = y ~ lbas * treat + lage + v4 + (1 | subj),
  data = epilep, family = poisson
)

confint(count_mod, parm = "beta", level = .99)

Extract deviance of galamm object

Description

Extract deviance of galamm object

Usage

## S3 method for class 'galamm'
deviance(object, ...)

Arguments

Value

A numeric value giving the deviance of the model fit.

See Also

logLik.galamm() for a function returning the log likelihood and deviance() for the generic function.

Other details of model fit: VarCorr(), coef.galamm(), confint.galamm(), factor_loadings.galamm(), family.galamm(), fitted.galamm(), fixef(), formula.galamm(), llikAIC(), logLik.galamm(), nobs.galamm(), predict.galamm(), print.VarCorr.galamm(), ranef.galamm(), residuals.galamm(), response(), sigma.galamm(), vcov.galamm()

Examples

# Linear mixed model with heteroscedastic residuals
mod <- galamm(
  formula = y ~ x + (1 | id),
  weights = ~ (1 | item),
  data = hsced
)

# Extract deviance
deviance(mod)

Diet Data

Description

Longitudinal epilepsy data from Morris et al. (1977). This documentation is based on Chapter 14.2 of Skrondal and Rabe-Hesketh (2004), where the dataset is used. See also Rabe-Hesketh et al. (2003).

Usage

diet

Format

diet A data frame with 236 rows and 7 columns:

id

Subject ID.

age

Age (standardized).

bus

Dummy variable indicating whether the subject is a bus driver or banking staff.

item

Integer indicating whether the outcome is fiber intake at time 1 (item = 1), fiber intake at time 2 (item = 2), or coronary heart disease (item = 3).

y

Outcome.

chd

Dummy variable indicating whether y is an indicator for coronary heart disease, coded as 0/1.

fiber

Dummy variable indicating whether y is a fiber measurement at either timepoint 1 or 2.

fiber2

Dummy variable indicating whether y is a fiber measurement at timepoint 2.

Source

http://www.gllamm.org/books/readme.html#14.2

References

Morris JN, Marr JW, Clayton DG (1977). “Diet and Heart: A Postscript.” Br Med J, 2(6098), 1307–1314. ISSN 0007-1447, 1468-5833, doi:10.1136/bmj.2.6098.1307.

Rabe-Hesketh S, Pickles A, Skrondal A (2003). “Correcting for Covariate Measurement Error in Logistic Regression Using Nonparametric Maximum Likelihood Estimation.” Statistical Modelling, 3(3), 215–232. ISSN 1471-082X, doi:10.1191/1471082X03st056oa.

Skrondal A, Rabe-Hesketh S (2004). Generalized Latent Variable Modeling, Interdisciplinary Statistics Series. Chapman and Hall/CRC, Boca Raton, Florida.

See Also

Other datasets: cognition, epilep, hsced, latent_covariates, latent_covariates_long, lifespan, mresp, mresp_hsced

Epilepsy Data

Description

Longitudinal epilepsy data from Leppik et al. (1987). This documentation is based on Chapter 11.3 of Skrondal and Rabe-Hesketh (2004), where the dataset is used.

Usage

epilep

Format

epilep A data frame with 236 rows and 7 columns:

subj

Subject ID.

y

Number of seizures.

treat

Dummy variable for treatment group.

visit

Time at visit.

v4

Dummy for visit 4.

lage

Logarithm of age.

lbas

Logarithm of a quarter of the number of seizures in the eight weeks preceding entry into the trial.

Source

http://www.gllamm.org/books/readme.html#11.3

References

Leppik IE, Dreifuss FE, Porter R, Bowman T, Santilli N, Jacobs M, Crosby C, Cloyd J, Stackman J, Graves N, Sutula T, Welty T, Vickery J, Brundage R, Gates J, Gumnit RJ, Gutierrez A (1987). “A Controlled Study of Progabide in Partial Seizures: Methodology and Results.” Neurology, 37(6), 963–963. ISSN 0028-3878, 1526-632X, doi:10.1212/WNL.37.6.963.

Skrondal A, Rabe-Hesketh S (2004). Generalized Latent Variable Modeling, Interdisciplinary Statistics Series. Chapman and Hall/CRC, Boca Raton, Florida.

See Also

Other datasets: cognition, diet, hsced, latent_covariates, latent_covariates_long, lifespan, mresp, mresp_hsced

Extract parameters from fitted model for use as initial values

Description

This function extracts parameter values from a fitted model object in a form that can be directly provided as initial values for a new model fit.

Usage

## S3 method for class 'galamm'
extract_optim_parameters(object)

Arguments

Value

A list object containing the following elements:

• theta Numerical vector of variance components, i.e., entries of the lower Cholesky form of the covariance matrix of random effects.

• beta Fixed regression coefficients.

• lambda Factor loadings.

• weights Weights for heteroscedastic residuals.

See Also

Other optimization functions: galamm_control()

Examples

# Fit linear mixed model with heteroscedastic residuals
mod <- galamm(
  formula = y ~ x + (1 | id),
  weights = ~ (1 | item),
  data = hsced
)

# Extract parameters
start <- extract_optim_parameters(mod)

# Fit again using the Nelder-Mead algorithm, using start as initial values:
mod_nm <- galamm(
  formula = y ~ x + (1 | id),
  weights = ~ (1 | item),
  data = hsced,
  start = start,
  control = galamm_control(method = "Nelder-Mead")
)

Extract factor loadings from galamm object

Description

Extract factor loadings from galamm object

Usage

## S3 method for class 'galamm'
factor_loadings(object)

Arguments

Details

This function has been named factor_loadings rather than just loadings to avoid conflict with stats::loadings.

Value

A matrix containing the estimated factor loadings with corresponding standard deviations.

Author(s)

The example for this function comes from PLmixed, with authors Nicholas Rockwood and Minjeong Jeon (Rockwood and Jeon 2019).

See Also

fixef.galamm() for fixed regression coefficients, confint.galamm() for confidence intervals, and coef.galamm() for coefficients more generally.

Other details of model fit: VarCorr(), coef.galamm(), confint.galamm(), deviance.galamm(), family.galamm(), fitted.galamm(), fixef(), formula.galamm(), llikAIC(), logLik.galamm(), nobs.galamm(), predict.galamm(), print.VarCorr.galamm(), ranef.galamm(), residuals.galamm(), response(), sigma.galamm(), vcov.galamm()

Examples

# Logistic mixed model with factor loadings, example from PLmixed
data("IRTsim", package = "PLmixed")

# Reduce data size for the example to run faster
IRTsub <- IRTsim[IRTsim$item < 4, ]
IRTsub <- IRTsub[sample(nrow(IRTsub), 300), ]
IRTsub$item <- factor(IRTsub$item)

# Fix loading for first item to 1, and estimate the two others freely
loading_matrix <- matrix(c(1, NA, NA), ncol = 1)

# Estimate model
mod <- galamm(y ~ item + (0 + ability | sid) + (0 + ability | school),
  data = IRTsub, family = binomial, load.var = "item",
  factor = "ability", lambda = loading_matrix
)

# Show estimated factor loadings, with standard errors
factor_loadings(mod)

Extract family or families from fitted galamm

Description

This function returns a list of families for an object of class galamm, returned from galamm.

Usage

## S3 method for class 'galamm'
family(object, ...)

Arguments

Value

A list of family objects.

See Also

galamm()

Other details of model fit: VarCorr(), coef.galamm(), confint.galamm(), deviance.galamm(), factor_loadings.galamm(), fitted.galamm(), fixef(), formula.galamm(), llikAIC(), logLik.galamm(), nobs.galamm(), predict.galamm(), print.VarCorr.galamm(), ranef.galamm(), residuals.galamm(), response(), sigma.galamm(), vcov.galamm()

Examples

# Mixed response model
loading_matrix <- matrix(c(1, NA), ncol = 1)
families <- c(gaussian, binomial)
family_mapping <- ifelse(mresp$itemgroup == "a", 1, 2)

mixed_resp <- galamm(
  formula = y ~ x + (0 + level | id),
  data = mresp,
  family = families,
  family_mapping = family_mapping,
  load.var = "itemgroup",
  lambda = loading_matrix,
  factor = "level"
)

# This model has two family objects
family(mixed_resp)

Extract model fitted values

Description

Extracts fitted values from a model including random effects.

Usage

## S3 method for class 'galamm'
fitted(object, ...)

Arguments

Value

A numerical vector with fit values for each row in the input data.

See Also

Other details of model fit: VarCorr(), coef.galamm(), confint.galamm(), deviance.galamm(), factor_loadings.galamm(), family.galamm(), fixef(), formula.galamm(), llikAIC(), logLik.galamm(), nobs.galamm(), predict.galamm(), print.VarCorr.galamm(), ranef.galamm(), residuals.galamm(), response(), sigma.galamm(), vcov.galamm()

Examples

# Linear mixed model with heteroscedastic residuals
mod <- galamm(
  formula = y ~ x + (1 | id),
  weights = ~ (1 | item),
  data = hsced
)

# Extract fitted values and plot against x
plot(hsced$x, fitted(mod))

Extract fixed effects from galamm objects

Description

Extract the fixed regression coefficients.

Usage

## S3 method for class 'galamm'
fixef(object, ...)

Arguments

Value

A named numeric vector containing the requested fixed effects.

See Also

ranef.galamm() for random effects, coef.galamm() for coefficients more generally, and confint.galamm() for confidence intervals.

Other details of model fit: VarCorr(), coef.galamm(), confint.galamm(), deviance.galamm(), factor_loadings.galamm(), family.galamm(), fitted.galamm(), formula.galamm(), llikAIC(), logLik.galamm(), nobs.galamm(), predict.galamm(), print.VarCorr.galamm(), ranef.galamm(), residuals.galamm(), response(), sigma.galamm(), vcov.galamm()

Examples

# Poisson GLMM
count_mod <- galamm(
  formula = y ~ lbas * treat + lage + v4 + (1 | subj),
  data = epilep, family = poisson
)

# Extract fixed effects
fixef(count_mod)

Extract formula from fitted galamm object

Description

Extract formula from fitted galamm object

Usage

## S3 method for class 'galamm'
formula(x, ...)

Arguments

Value

The formula used to fit the model.

See Also

Other details of model fit: VarCorr(), coef.galamm(), confint.galamm(), deviance.galamm(), factor_loadings.galamm(), family.galamm(), fitted.galamm(), fixef(), llikAIC(), logLik.galamm(), nobs.galamm(), predict.galamm(), print.VarCorr.galamm(), ranef.galamm(), residuals.galamm(), response(), sigma.galamm(), vcov.galamm()

Examples

# Mixed response model ------------------------------------------------------

# The mresp dataset contains a mix of binomial and Gaussian responses.

# We need to estimate a factor loading which scales the two response types.
loading_matrix <- matrix(c(1, NA), ncol = 1)

# Define mapping to families.
families <- c(gaussian, binomial)
family_mapping <- ifelse(mresp$itemgroup == "a", 1, 2)


# Fit the model
mod <- galamm(
  formula = y ~ x + (0 + level | id),
  data = mresp,
  family = families,
  family_mapping = family_mapping,
  factor = "level",
  load.var = "itemgroup",
  lambda = loading_matrix
)

# Formula
formula(mod)

Fit a generalized additive latent and mixed model

Description

This function fits a generalized additive latent and mixed model (GALAMMs), as described in Sørensen et al. (2023). The building blocks of these models are generalized additive mixed models (GAMMs) (Wood 2017), of which generalized linear mixed models (Breslow and Clayton 1993; Harville 1977; Henderson 1975; Laird and Ware 1982) are special cases. GALAMMs extend upon GAMMs by allowing factor structures, as commonly used to model hypothesized latent traits underlying observed measurements. In this sense, GALAMMs are an extension of generalized linear latent and mixed models (GLLAMMs) (Skrondal and Rabe-Hesketh 2004; Rabe-Hesketh et al. 2004) which allows semiparametric estimation. The implemented algorithm used to compute model estimates is described in Sørensen et al. (2023), and is an extension of the algorithm used for fitting generalized linear mixed models by the lme4 package (Bates et al. 2015). The syntax used to define factor structures is based on that used by the PLmixed package, which is detailed in Rockwood and Jeon (2019).

Usage

galamm(
  formula,
  weights = NULL,
  data,
  family = gaussian,
  family_mapping = rep(1, nrow(data)),
  load.var = NULL,
  lambda = NULL,
  factor = NULL,
  factor_interactions = NULL,
  na.action = getOption("na.action"),
  start = NULL,
  control = galamm_control()
)

Arguments

Value

A model object of class galamm, containing the following elements:

• call the matched call used when fitting the model.

• random_effects a list containing the following two elements:

  • b random effects in original parametrization.

  • u random effects standardized to have identity covariance matrix.

• model a list with various elements related to the model setup and fit:

  • deviance deviance of final model.

  • deviance_residuals deviance residuals of the final model.

  • df degrees of freedom of model.

  • family a list of one or more family objects, as specified in the family arguments to galamm.

  • factor_interactions List of formulas specifying interactions between latent and observed variables, as provided to the argument factor_interactions to galamm. If not provided, it is NULL.

  • fit a numeric vector with fitted values.

  • fit_population a numeric vector with fitted values excluding random effects.

  • hessian Hessian matrix of final model, i.e., the second derivative of the log-likelihood with respect to all model parameters.

  • lmod Linear model object returned by lme4::lFormula, which is used internally for setting up the models.

  • loglik Log-likelihood of final model.

  • n Number of observations.

  • pearson_residual Pearson residuals of final model.

  • reduced_hessian Logical specifying whether the full Hessian matrix was computed, or a Hessian matrix with derivatives only with respect to beta and lambda.

  • response A numeric vector containing the response values used when fitting the model.

  • weights_object Object with weights used in model fitting. Is NULL when no weights were used.

• parameters A list object with model parameters and related information:

  • beta_inds Integer vector specifying the indices of fixed regression coefficients among the estimated model parameters.

  • dispersion_parameter One or more dispersion parameters of the final model.

  • lambda_dummy Dummy matrix of factor loadings, which shows the structure of the loading matrix that was supplied in the lambda arguments.

  • lambda_inds Integer vector specifying the indices of factor loadings among the estimated model parameters.

  • lambda_interaction_inds Integer vector specifying the indices of regression coefficients for interactions between latent and observed variables.

  • parameter_estimates Numeric vector of final parameter estimates.

  • parameter_names Names of all parameters estimates.

  • theta_inds Integer vector specifying the indices of variance components among the estimated model parameters. Technically these are the entries of the Cholesky decomposition of the covariance matrix.

  • weights_inds Integer vector specifying the indices of estimated weights (used in heteroscedastic Gaussian models) among the estimated model parameters.

• gam List containing information about smooth terms in the model. If no smooth terms are contained in the model, then it is a list of length zero.

References

Bates DM, Mächler M, Bolker B, Walker S (2015). “Fitting Linear Mixed-Effects Models Using Lme4.” Journal of Statistical Software, 67(1), 1–48. ISSN 1548-7660, doi:10.18637/jss.v067.i01.

Breslow NE, Clayton DG (1993). “Approximate Inference in Generalized Linear Mixed Models.” Journal of the American Statistical Association, 88(421), 9–25. ISSN 0162-1459, doi:10.2307/2290687.

Harville DA (1977). “Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems.” Journal of the American Statistical Association, 72(358), 320–338. ISSN 0162-1459, doi:10.2307/2286796.

Henderson CR (1975). “Best Linear Unbiased Estimation and Prediction under a Selection Model.” Biometrics, 31(2), 423–447. ISSN 0006-341X, doi:10.2307/2529430.

Laird NM, Ware JH (1982). “Random-Effects Models for Longitudinal Data.” Biometrics, 38(4), 963–974. ISSN 0006-341X, doi:10.2307/2529876.

Rabe-Hesketh S, Skrondal A, Pickles A (2004). “Generalized Multilevel Structural Equation Modeling.” Psychometrika, 69(2), 167–190. ISSN 1860-0980, doi:10.1007/BF02295939.

Rockwood NJ, Jeon M (2019). “Estimating Complex Measurement and Growth Models Using the R Package PLmixed.” Multivariate Behavioral Research, 54(2), 288–306. ISSN 0027-3171, doi:10.1080/00273171.2018.1516541.

Skrondal A, Rabe-Hesketh S (2004). Generalized Latent Variable Modeling, Interdisciplinary Statistics Series. Chapman and Hall/CRC, Boca Raton, Florida.

Sørensen Ø, Fjell AM, Walhovd KB (2023). “Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models.” Psychometrika, 88(2), 456–486. ISSN 1860-0980, doi:10.1007/s11336-023-09910-z.

Wood SN (2017). Generalized Additive Models: An Introduction with R, 2 edition. Chapman and Hall/CRC.

See Also

Other modeling functions: s(), t2()

Examples

# Mixed response model ------------------------------------------------------

# The mresp dataset contains a mix of binomial and Gaussian responses.

# We need to estimate a factor loading which scales the two response types.
loading_matrix <- matrix(c(1, NA), ncol = 1)

# Define mapping to families.
families <- c(gaussian, binomial)
family_mapping <- ifelse(mresp$itemgroup == "a", 1, 2)


# Fit the model
mod <- galamm(
  formula = y ~ x + (0 + level | id),
  data = mresp,
  family = families,
  family_mapping = family_mapping,
  factor = "level",
  load.var = "itemgroup",
  lambda = loading_matrix
)

# Summary information
summary(mod)


# Heteroscedastic model -----------------------------------------------------
# Residuals allowed to differ according to the item variable
# We also set the initial value of the random intercept standard deviation
# to 1
mod <- galamm(
  formula = y ~ x + (1 | id), weights = ~ (1 | item),
  data = hsced, start = list(theta = 1)
)
summary(mod)

# Generalized additive mixed model with factor structures -------------------

# The cognition dataset contains simulated measurements of three latent
# time-dependent processes, corresponding to individuals' abilities in
# cognitive domains. We focus here on the first domain, and take a single
# random timepoint per person:
dat <- subset(cognition, domain == 1)
dat <- split(dat, f = dat$id)
dat <- lapply(dat, function(x) x[x$timepoint %in% sample(x$timepoint, 1), ])
dat <- do.call(rbind, dat)
dat$item <- factor(dat$item)

# At each timepoint there are three items measuring ability in the cognitive
# domain. We fix the factor loading for the first measurement to one, and
# estimate the remaining two. This is specified in the loading matrix.
loading_matrix <- matrix(c(1, NA, NA), ncol = 1)

# We can now estimate the model.
mod <- galamm(
  formula = y ~ 0 + item + sl(x, factor = "loading") +
    (0 + loading | id),
  data = dat,
  load.var = "item",
  lambda = loading_matrix,
  factor = "loading"
)

# We can plot the estimated smooth term
plot_smooth(mod, shade = TRUE)


# Interaction between observed and latent covariates ------------------------
# Define the loading matrix
lambda <- matrix(c(1, NA, NA), ncol = 1)

# Define the regression functions, one for each row in the loading matrix
factor_interactions <- list(~1, ~1, ~x)

# Fit the model
mod <- galamm(
  formula = y ~ type + x:response + (0 + loading | id),
  data = latent_covariates,
  load.var = "type",
  lambda = lambda,
  factor = "loading",
  factor_interactions = factor_interactions
)

# The summary output now include an interaction between the latent variable
# and x, for predicting the third element in "type"
summary(mod)

Control values for galamm fit

Description

This function can be called for controling the optimization procedure used when fitting GALAMMs using galamm.

Usage

galamm_control(
  optim_control = list(),
  method = c("L-BFGS-B", "Nelder-Mead"),
  maxit_conditional_modes = 10,
  pirls_tol_abs = 0.01,
  reduced_hessian = FALSE
)

Arguments

Value

Object of class galamm_control, which typically will be provided as an argument to galamm.

References

Bates DM, Mächler M, Bolker B, Walker S (2015). “Fitting Linear Mixed-Effects Models Using Lme4.” Journal of Statistical Software, 67(1), 1–48. ISSN 1548-7660, doi:10.18637/jss.v067.i01.

BROYDEN CG (1970). “The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations.” IMA Journal of Applied Mathematics, 6(1), 76–90. ISSN 0272-4960, doi:10.1093/imamat/6.1.76.

Byrd RH, Lu P, Nocedal J, Zhu C (1995). “A Limited Memory Algorithm for Bound Constrained Optimization.” SIAM Journal on Scientific Computing, 16(5), 1190–1208. ISSN 1064-8275, doi:10.1137/0916069.

Fletcher R (1970). “A New Approach to Variable Metric Algorithms.” The Computer Journal, 13(3), 317–322. ISSN 0010-4620, doi:10.1093/comjnl/13.3.317.

Goldfarb D (1970). “A Family of Variable-Metric Methods Derived by Variational Means.” Mathematics of Computation, 24(109), 23–26. ISSN 0025-5718, 1088-6842, doi:10.1090/S0025-5718-1970-0258249-6.

Nelder JA, Mead R (1965). “A Simplex Method for Function Minimization.” The Computer Journal, 7(4), 308–313. ISSN 0010-4620, doi:10.1093/comjnl/7.4.308.

Shanno DF (1970). “Conditioning of Quasi-Newton Methods for Function Minimization.” Mathematics of Computation, 24(111), 647–656. ISSN 0025-5718, 1088-6842, doi:10.1090/S0025-5718-1970-0274029-X.

See Also

galamm()

Other optimization functions: extract_optim_parameters.galamm()

Examples

# Define control object with quite a high degree of verbosity (trace = 6)
# and using the last 20 BFGS updates to estimate the Hessian in L-BFGS-B.
control <- galamm_control(optim_control = list(trace = 6, lmm = 20))

Example Data with Heteroscedastic Residuals

Description

Simulated dataset with residual standard deviation that varies between items.

Usage

hsced

Format

hsced A data frame with 1200 rows and 5 columns:

id

Subject ID.

age

Timepoint.

item

Item indicator.

x

Explanatory variable

y

Outcome.

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

See Also

Other datasets: cognition, diet, epilep, latent_covariates, latent_covariates_long, lifespan, mresp, mresp_hsced

Simulated Data with Latent and Observed Covariates Interaction

Description

Simulated dataset for use in examples and testing with a latent covariate interacting with an observed covariate.

Usage

latent_covariates

Format

latent_covariates A data frame with 600 rows and 5 columns:

id

Subject ID.

type

Type of observation in the y variable. If it equals "measurement1" or "measurement2" then the observation is a measurement of the latent variable. If it equals "response", then the observation is the actual response.

x

Explanatory variable.

y

Observed response. Note, this includes both the actual response, and the measurements of the latent variable, since mathematically they are all treated as responses.

response

Dummy variable indicating whether the given row is a response or not.

See Also

Other datasets: cognition, diet, epilep, hsced, latent_covariates_long, lifespan, mresp, mresp_hsced

Simulated Longitudinal Data with Latent and Observed Covariates Interaction

Description

Simulated dataset for use in examples and testing with a latent covariate interacting with an observed covariate. In this data, each response has been measured six times for each subject.

Usage

latent_covariates_long

Format

latent_covariates_long A data frame with 800 rows and 5

columns:

id

Subject ID.

type

Type of observation in the y variable. If it equals "measurement1" or "measurement2" then the observation is a measurement of the latent variable. If it equals "response", then the observation is the actual response.

x

Explanatory variable.

y

Observed response. Note, this includes both the actual response, and the measurements of the latent variable, since mathematically they are all treated as responses.

response

Dummy variable indicating whether the given row is a response or not.

See Also

Other datasets: cognition, diet, epilep, hsced, latent_covariates, lifespan, mresp, mresp_hsced

Simulated Dataset with Lifespan Trajectories of Three Cognitive Domains

Description

This dataset is simulated based on the data used in Section 4.1 of Sørensen et al. (2023).

Usage

lifespan

Format

lifespan A data frame with 54,457 rows and 7 columns:

id

Subject ID.

domain

Cognitive domain being measured. One of "epmem" for episodic memory, "wmem" for working memory and "execfun" for executive function/speed.

timepoint

Integer indicating the timepoint number.

age

Age of participant at the timepoint.

test

The particular test at this observation.

y

Response. For "epmem" and "wmem" this is the number of successes in 16 trials. For "execfun" it is the time in seconds to complete the task.

retest

Integer indicating whether the participant has taken the test at a previous timepoint.

domainepmem

Dummy variable for domain=="epmem".

domainwmem

Dummy variable for domain=="wmem".

domainexecfun

Dummy variable for domain=="execfun".

References

Sørensen Ø, Fjell AM, Walhovd KB (2023). “Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models.” Psychometrika, 88(2), 456–486. ISSN 1860-0980, doi:10.1007/s11336-023-09910-z.

See Also

Other datasets: cognition, diet, epilep, hsced, latent_covariates, latent_covariates_long, mresp, mresp_hsced

Extract log likelihood, AIC, and related statistics from a GALAMM

Description

This function is assembles the values used by summary.galamm.

Usage

llikAIC(object)

Arguments

Value

A list containing AIC, BIC, log likelihood, deviance and residual degrees of freedom.

See Also

Other details of model fit: VarCorr(), coef.galamm(), confint.galamm(), deviance.galamm(), factor_loadings.galamm(), family.galamm(), fitted.galamm(), fixef(), formula.galamm(), logLik.galamm(), nobs.galamm(), predict.galamm(), print.VarCorr.galamm(), ranef.galamm(), residuals.galamm(), response(), sigma.galamm(), vcov.galamm()

Extract Log-Likelihood of galamm Object

Description

Extract Log-Likelihood of galamm Object

Usage

## S3 method for class 'galamm'
logLik(object, ...)

Arguments

Value

Object of class logLik

See Also

deviance.galamm() for a function returning deviance and logLik() for the generic function.

Other details of model fit: VarCorr(), coef.galamm(), confint.galamm(), deviance.galamm(), factor_loadings.galamm(), family.galamm(), fitted.galamm(), fixef(), formula.galamm(), llikAIC(), nobs.galamm(), predict.galamm(), print.VarCorr.galamm(), ranef.galamm(), residuals.galamm(), response(), sigma.galamm(), vcov.galamm()

Examples

# Linear mixed model with heteroscedastic residuals
mod <- galamm(
  formula = y ~ x + (1 | id),
  weights = ~ (1 | item),
  data = hsced
)

# Extract log likelihood
logLik(mod)

Simulated Mixed Response Data

Description

Very basic mixed response dataset with one set of normally distributed responses and one set of binomially distributed responses.

Usage

mresp

Format

mresp A data frame with 4000 rows and 5 columns:

id

Subject ID.

x

Predictor variable.

y

Response.

itemgroup

Factor variable which equals "a" for the normally distributed responses and "b" for the binomially distributed response (with 1 trial).

See Also

Other datasets: cognition, diet, epilep, hsced, latent_covariates, latent_covariates_long, lifespan, mresp_hsced

Simulated Mixed Response Data with Heteroscedastic Residuals

Description

Mixed response dataset with one set of normally distributed responses and one set of binomially distributed responses. The normally distributed response follow two different residual standard deviations.

Usage

mresp_hsced

Format

mresp A data frame with 4000 rows and 5 columns:

id

Subject ID.

x

Predictor variable.

y

Response.

itemgroup

Factor variable which equals "a" for the normally distributed responses and "b" for the binomially distributed response (with 1 trial).

grp

Grouping variable denoting which of the two residual standard deviations apply. Only relevant for the normally distributed responses.

isgauss

Dummy variable indicating whether the observation on the given line is normally (Gaussian) distributed or not.

See Also

Other datasets: cognition, diet, epilep, hsced, latent_covariates, latent_covariates_long, lifespan, mresp

Extract the Number of Observations from a galamm Fit

Description

Extract the Number of Observations from a galamm Fit

Usage

## S3 method for class 'galamm'
nobs(object, ...)

Arguments

Value

A number

See Also

Other details of model fit: VarCorr(), coef.galamm(), confint.galamm(), deviance.galamm(), factor_loadings.galamm(), family.galamm(), fitted.galamm(), fixef(), formula.galamm(), llikAIC(), logLik.galamm(), predict.galamm(), print.VarCorr.galamm(), ranef.galamm(), residuals.galamm(), response(), sigma.galamm(), vcov.galamm()

Examples

# Example model from lme4
data(sleepstudy, package = "lme4")
fm1 <- galamm(Reaction ~ Days + (Days | Subject), data = sleepstudy)

# There are 180 observations, which matches the number of rows in sleepstudy
nobs(fm1)
nrow(sleepstudy)

Diagnostic plots for galamm objects

Description

Diagnostic plots for galamm objects

Usage

## S3 method for class 'galamm'
plot(x, ...)

Arguments

Value

A plot is displayed.

See Also

residuals.galamm() for extracting residuals and plot() for the generic function.

Other summary functions: anova.galamm(), plot_smooth.galamm(), print.galamm(), print.summary.galamm(), summary.galamm()

Examples

# Linear mixed model example from lme4
data("sleepstudy", package = "lme4")
mod <- galamm(Reaction ~ Days + (Days | Subject), data = sleepstudy)

# Diagnostic plot
plot(mod)

Plot smooth terms for galamm fits

Description

Plots smooth terms of a fitted galamm object. This function is a thin wrapper around mgcv::plot.gam (Wood 2017).

Usage

## S3 method for class 'galamm'
plot_smooth(object, ...)

Arguments

Value

A plot is displayed on the screen.

References

Wood SN (2017). Generalized Additive Models: An Introduction with R, 2 edition. Chapman and Hall/CRC.

See Also

Other summary functions: anova.galamm(), plot.galamm(), print.galamm(), print.summary.galamm(), summary.galamm()

Examples

# Generalized additive mixed model with factor structures -------------------

# The cognition dataset contains simulated measurements of three latent
# time-dependent processes, corresponding to individuals' abilities in
# cognitive domains. We focus here on the first domain, and take a single
# random timepoint per person:
dat <- subset(cognition, domain == 1)
dat <- split(dat, f = dat$id)
dat <- lapply(dat, function(x) x[x$timepoint %in% sample(x$timepoint, 1), ])
dat <- do.call(rbind, dat)
dat$item <- factor(dat$item)

# At each timepoint there are three items measuring ability in the cognitive
# domain. We fix the factor loading for the first measurement to one, and
# estimate the remaining two. This is specified in the loading matrix.
loading_matrix <- matrix(c(1, NA, NA), ncol = 1)

# We can now estimate the model.
mod <- galamm(
  formula = y ~ 0 + item + sl(x, factor = "loading") +
    (0 + loading | id),
  data = dat,
  load.var = "item",
  lambda = loading_matrix,
  factor = "loading"
)

# We can plot the estimated smooth term
plot_smooth(mod, shade = TRUE)

# We can turn off the rug at the bottom
plot_smooth(mod, shade = TRUE, rug = FALSE)

Predictions from a model at new data values

Description

Predictions are given at the population level, i.e., with random effects set to zero. For fitted models including random effects, see fitted.galamm. For mixed response models, only predictions on the scale of the linear predictors is supported.

Usage

## S3 method for class 'galamm'
predict(object, newdata = NULL, type = c("link", "response"), ...)

Arguments

Value

A numeric vector of predicted values.

See Also

fitted.galamm() for model fits, residuals.galamm() for residuals, and predict() for the generic function.

Other details of model fit: VarCorr(), coef.galamm(), confint.galamm(), deviance.galamm(), factor_loadings.galamm(), family.galamm(), fitted.galamm(), fixef(), formula.galamm(), llikAIC(), logLik.galamm(), nobs.galamm(), print.VarCorr.galamm(), ranef.galamm(), residuals.galamm(), response(), sigma.galamm(), vcov.galamm()

Examples

# Poisson GLMM
count_mod <- galamm(
  formula = y ~ lbas * treat + lage + v4 + (1 | subj),
  data = epilep, family = poisson
)

# Plot response versus link:
plot(
  predict(count_mod, type = "link"),
  predict(count_mod, type = "response")
)

# Predict on a new dataset
nd <- data.frame(lbas = c(.3, .2), treat = c(0, 1), lage = 0.2, v4 = -.2)
predict(count_mod, newdata = nd)
predict(count_mod, newdata = nd, type = "response")

Print method for variance-covariance objects

Description

Print method for variance-covariance objects

Usage

## S3 method for class 'VarCorr.galamm'
print(
  x,
  digits = max(3, getOption("digits") - 2),
  comp = c("Std.Dev.", "Variance"),
  corr = any(comp == "Std.Dev."),
  ...
)

Arguments

Value

The variance-covariance information is printed to the console and the argument x is silently returned.

Author(s)

This function is derived from lme4:::print.VarCorr.merMod written by Douglas M. Bates, Martin Maechler, Ben Bolker, and Steve Walker.

References

Bates DM, Mächler M, Bolker B, Walker S (2015). “Fitting Linear Mixed-Effects Models Using Lme4.” Journal of Statistical Software, 67(1), 1–48. ISSN 1548-7660, doi:10.18637/jss.v067.i01.

See Also

VarCorr.galamm() for the function creating the variance-covariance objects.

Other details of model fit: VarCorr(), coef.galamm(), confint.galamm(), deviance.galamm(), factor_loadings.galamm(), family.galamm(), fitted.galamm(), fixef(), formula.galamm(), llikAIC(), logLik.galamm(), nobs.galamm(), predict.galamm(), ranef.galamm(), residuals.galamm(), response(), sigma.galamm(), vcov.galamm()

Examples

# Linear mixed model with heteroscedastic residuals
mod <- galamm(
  formula = y ~ x + (1 | id),
  weights = ~ (1 | item),
  data = hsced
)

# Extract information on variance and covariance
VarCorr(mod)

Print method for GALAMM fits

Description

Print method for GALAMM fits

Usage

## S3 method for class 'galamm'
print(x, ...)

Arguments

Value

Summary printed to screen. Invisibly returns the argument x.

See Also

summary.galamm() for the summary function and print() for the generic.

Other summary functions: anova.galamm(), plot.galamm(), plot_smooth.galamm(), print.summary.galamm(), summary.galamm()

Examples

# Linear mixed model with heteroscedastic residuals
mod <- galamm(
  formula = y ~ x + (1 | id),
  weights = ~ (1 | item),
  data = hsced
)

print(mod)

Print method for summary GALAMM fits

Description

Print method for summary GALAMM fits

Usage

## S3 method for class 'summary.galamm'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

Value

Summary printed to screen. Invisibly returns the argument x.

Author(s)

Some of the code for producing summary information has been derived from the summary methods of mgcv (author: Simon Wood) and lme4 (Bates et al. 2015) (authors: Douglas M. Bates, Martin Maechler, Ben Bolker, and Steve Walker).

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

See Also

summary.galamm() for the summary function and print() for the generic function.

Other summary functions: anova.galamm(), plot.galamm(), plot_smooth.galamm(), print.galamm(), summary.galamm()

Examples

# Linear mixed model with heteroscedastic residuals
mod <- galamm(
  formula = y ~ x + (1 | id),
  weights = ~ (1 | item),
  data = hsced
)

summary(mod)

Extract random effects from galamm object.

Description

Extract random effects from galamm object.

Usage

## S3 method for class 'galamm'
ranef(object, ...)

Arguments

Value

An object of class ranef.galamm, containing the requested random effects.

Author(s)

This function is derived from lme4::ranef.merMod, written by Douglas Bates, Martin Maechler, Ben Bolker, Steve Walker.

References

Bates DM, Mächler M, Bolker B, Walker S (2015). “Fitting Linear Mixed-Effects Models Using Lme4.” Journal of Statistical Software, 67(1), 1–48. ISSN 1548-7660, doi:10.18637/jss.v067.i01.

See Also

fixef.galamm() for fixed effects and coef.galamm() for coefficients more generally.

Other details of model fit: VarCorr(), coef.galamm(), confint.galamm(), deviance.galamm(), factor_loadings.galamm(), family.galamm(), fitted.galamm(), fixef(), formula.galamm(), llikAIC(), logLik.galamm(), nobs.galamm(), predict.galamm(), print.VarCorr.galamm(), residuals.galamm(), response(), sigma.galamm(), vcov.galamm()

Examples

# Poisson GLMM
count_mod <- galamm(
  formula = y ~ lbas * treat + lage + v4 + (1 | subj),
  data = epilep, family = poisson
)

# Extract random effects
ranef(count_mod)

Residuals of galamm objects

Description

Residuals of galamm objects

Usage

## S3 method for class 'galamm'
residuals(object, type = c("pearson", "deviance"), ...)

Arguments

Value

Numeric vector of residual values.

See Also

fitted.galamm() for model fitted values, predict.galamm() for model predictions, and plot.galamm() for diagnostic plots. The generic function is residuals().

Other details of model fit: VarCorr(), coef.galamm(), confint.galamm(), deviance.galamm(), factor_loadings.galamm(), family.galamm(), fitted.galamm(), fixef(), formula.galamm(), llikAIC(), logLik.galamm(), nobs.galamm(), predict.galamm(), print.VarCorr.galamm(), ranef.galamm(), response(), sigma.galamm(), vcov.galamm()

Examples

# Poisson GLMM
count_mod <- galamm(
  formula = y ~ lbas * treat + lage + v4 + (1 | subj),
  data = epilep, family = poisson
)

# Extract residuals
residuals(count_mod)

Extract response values

Description

Extracts response values from a model.

Usage

response(object, ...)

Arguments

Value

A numerical vector with fit response values for each row in the input data.

See Also

Other details of model fit: VarCorr(), coef.galamm(), confint.galamm(), deviance.galamm(), factor_loadings.galamm(), family.galamm(), fitted.galamm(), fixef(), formula.galamm(), llikAIC(), logLik.galamm(), nobs.galamm(), predict.galamm(), print.VarCorr.galamm(), ranef.galamm(), residuals.galamm(), sigma.galamm(), vcov.galamm()

Examples

# Linear mixed model with heteroscedastic residuals
mod <- galamm(
  formula = y ~ x + (1 | id),
  weights = ~ (1 | item),
  data = hsced
)

# Plot response versus fitted values
plot(fitted(mod), response(mod))

Set up smooth term with factor loading

Description

This is a very thin wrapper around mgcv::s. It enables the specification of loading variables for smooth terms. The last letter "l", which stands for "loading", has been added to avoid namespace conflicts with mgcv and gamm4.

Usage

sl(..., factor = NULL)

Arguments

Details

The documentation of the function mgcv::s should be consulted for details on how to properly set up smooth terms. In particular, note that these terms distinguish between ordered and unordered factor terms in the by variable, which can be provided in ... and is forwarded to mgcv::s.

Value

An object of class xx.smooth.spec, where xx is a basis identifying code given by the bs argument of s. It differs from the smooth returned by mgcv::s in that it has an additional attribute named "factor" which specifies any factor loading which this smooth term should be multiplied with in order to produce the observed outcome.

References

Wood SN (2003). “Thin Plate Regression Splines.” Journal of the Royal Statistical Society. Series B (Statistical Methodology), 65(1), 95–114. ISSN 1369-7412.

Wood SN (2017). Generalized Additive Models: An Introduction with R, 2 edition. Chapman and Hall/CRC.

See Also

Other modeling functions: galamm(), t2()

Examples

# Linear mixed model with factor structures
dat <- subset(cognition, domain == 1 & timepoint == 1)
loading_matrix <- matrix(c(1, NA, NA), ncol = 1)


# Model with four thin-plate regression splines as basis functions
mod <- galamm(
  formula = y ~ 0 + item + sl(x, k = 4, factor = "loading"),
  data = dat,
  load.var = "item",
  lambda = loading_matrix,
  factor = "loading"
)

# Model with four cubic regression splines as basis functions
mod <- galamm(
  formula = y ~ 0 + item +
    sl(x, bs = "cr", k = 4, factor = "loading"),
  data = dat,
  load.var = "item",
  lambda = loading_matrix,
  factor = "loading"
)

Extract square root of dispersion parameter from galamm object

Description

Extracts the square root of the dispersion parameter(s) from an object of class galamm, returned from galamm. In the case of conditionally Gaussian responses, this is the residual standard deviation. When there are multiple dispersion parameters, e.g., with mixed response type models, the square root of all of them are returned in a numeric vector.

Usage

## S3 method for class 'galamm'
sigma(object, ...)

Arguments

Value

The square root of one or more dispersion parameters.

See Also

galamm()

Other details of model fit: VarCorr(), coef.galamm(), confint.galamm(), deviance.galamm(), factor_loadings.galamm(), family.galamm(), fitted.galamm(), fixef(), formula.galamm(), llikAIC(), logLik.galamm(), nobs.galamm(), predict.galamm(), print.VarCorr.galamm(), ranef.galamm(), residuals.galamm(), response(), vcov.galamm()

Examples

# Linear mixed model with heteroscedastic residuals
mod <- galamm(
  formula = y ~ x + (1 | id),
  weights = ~ (1 | item),
  data = hsced
)

# Extract residual standard deviation.
sigma(mod)

# The residual standard deviation applies to the base case. The variance
# function shown in the model output shows the estimated multiplier for
# various grouping levels:
summary(mod)

Summarizing GALAMM fits

Description

Summary method for class "galamm".

Usage

## S3 method for class 'galamm'
summary(object, ...)

Arguments

Value

A list of summary statistics of the fitted model of class summary.galamm, containing the following elements:

• AICtab a table of model fit measures, returned by llikAIC.

• call the matched call used when fitting the model.

• fixef a matrix with fixed effect estimated, returned by fixef.

• gam List containing information about smooth terms in the model. If no smooth terms are contained in the model, then it is a list of length zero.

• model a list with various elements related to the model setup and fit. See ?galamm for details.

• parameters A list object with model parameters and related information. See ?galamm for details.

• Lambda An object containing the estimated factor loadings. Returned from factor_loadings.galamm. If there are no estimated factor loadings, then this object is NULL.

• random_effects a list containing the random effects. See ?galamm for details.

• VarCorr An object of class VarCorr.galamm, returned from VarCorr.galamm.

• weights An object containing information about estimated variance functions, when there are heteroscedastic residuals. Otherwise the object is NULL.

Author(s)

Some of the code for producing summary information has been derived from the summary methods of mgcv (author: Simon Wood) and lme4 (Bates et al. 2015) (authors: Douglas M. Bates, Martin Maechler, Ben Bolker, and Steve Walker).

See Also

print.summary.galamm() for the print method and summary() for the generic.

Other summary functions: anova.galamm(), plot.galamm(), plot_smooth.galamm(), print.galamm(), print.summary.galamm()

Examples

# Linear mixed model with heteroscedastic residuals
mod <- galamm(
  formula = y ~ x + (1 | id),
  weights = ~ (1 | item),
  data = hsced
)

summary(mod)

Set up smooth term with factor loading

Description

This is a very thin wrapper around mgcv::t2. It enables the specification of loading variables for smooth terms. The last letter "l", which stands for "loading", has been added to avoid namespace conflicts with mgcv and gamm4.

Usage

t2l(..., factor = NULL)

Arguments

Details

The documentation of the function mgcv::t2 should be consulted for details on how to properly set up smooth terms. In particular, note that these terms distinguish between ordered and unordered factor terms in the by variable, which can be provided in ... and is forwarded to mgcv::t2.

Value

An object of class xx.smooth.spec, where xx is a basis identifying code given by the bs argument of t2. It differs from the smooth returned by mgcv::s in that it has an additional attribute named "factor" which specifies any factor loading which this smooth term should be multiplied with in order to produce the observed outcome.

References

Wood SN (2003). “Thin Plate Regression Splines.” Journal of the Royal Statistical Society. Series B (Statistical Methodology), 65(1), 95–114. ISSN 1369-7412.

Wood SN (2017). Generalized Additive Models: An Introduction with R, 2 edition. Chapman and Hall/CRC.

See Also

Other modeling functions: galamm(), s()

Examples

# Linear mixed model with factor structures
dat <- subset(cognition, domain == 1 & timepoint == 1)
loading_matrix <- matrix(c(1, NA, NA), ncol = 1)

# Model with four cubic regression splines as basis functions
mod <- galamm(
  formula = y ~ 0 + item + t2l(x, k = 4, factor = "loading"),
  data = dat,
  load.var = "item",
  lambda = loading_matrix,
  factor = "loading"
)

# Model with four thin-plate regression splines as basis functions
mod <- galamm(
  formula = y ~ 0 + item +
    t2l(x, bs = "tp", k = 4, factor = "loading"),
  data = dat,
  load.var = "item",
  lambda = loading_matrix,
  factor = "loading"
)

Calculate variance-covariance matrix for GALAMM fit

Description

Calculate variance-covariance matrix for GALAMM fit

Usage

## S3 method for class 'galamm'
vcov(object, parm = "beta", ...)

Arguments

Value

A variance-covariance matrix.

See Also

confint.galamm() for the method computing confidence intervals. See vcov() for the generic function.

Other details of model fit: VarCorr(), coef.galamm(), confint.galamm(), deviance.galamm(), factor_loadings.galamm(), family.galamm(), fitted.galamm(), fixef(), formula.galamm(), llikAIC(), logLik.galamm(), nobs.galamm(), predict.galamm(), print.VarCorr.galamm(), ranef.galamm(), residuals.galamm(), response(), sigma.galamm()

Examples

# Linear mixed model with heteroscedastic residuals
mod <- galamm(
  formula = y ~ x + (1 | id),
  weights = ~ (1 | item),
  data = hsced
)

# Extract covariance matrix for fixed regression coefficients
vcov(mod, parm = "beta")

# and then for weights, which gives us the variance.
vcov(mod, parm = "weights")