Help for package gppm

Version:

0.3.0

Title:

Gaussian Process Panel Modeling

Description:

Provides an implementation of Gaussian process panel modeling (GPPM). GPPM is described in Karch, Brandmaier & Voelkle (2020; <doi:10.3389/fpsyg.2020.00351>) and Karch (2016; <doi:10.18452/17641>). Essentially, GPPM is Gaussian process based modeling of longitudinal panel data. 'gppm' also supports regular Gaussian process regression (with a focus on flexible model specification), and multi-task learning.

Depends:

R (≥ 3.5)

Imports:

ggplot2 (≥ 2.2.1), ggthemes (≥ 3.5.0), MASS (≥ 7.3-49), methods, mvtnorm (≥ 1.0-8), Rcpp (≥ 0.12.0), RcppParallel (≥ 5.0.1), rstan (≥ 2.18.1), rstantools (≥ 2.4.0), stats,

Suggests:

testthat (≥ 2.0.0), knitr (≥ 1.20), rmarkdown (≥ 1.10), roxygen2 (≥ 6.0.1), testit (≥ 0.12), covr

LinkingTo:

BH (≥ 1.66.0), Rcpp (≥ 0.12.0), RcppEigen (≥ 0.3.3.3.0), RcppParallel (≥ 5.0.1), rstan (≥ 2.18.1), StanHeaders (≥ 2.18.0)

License:

GPL-3 | file LICENSE

LazyData:

true

URL:

https://github.com/karchjd/gppm

BugReports:

https://github.com/karchjd/gppm/issues

RoxygenNote:

7.3.2

Encoding:

UTF-8

Biarch:

true

SystemRequirements:

GNU make

NeedsCompilation:

Packaged:

2025-08-21 14:53:56 UTC; karch

Author:

Julian D. Karch [aut, cre, cph]

Maintainer:

Julian D. Karch <j.d.karch@fsw.leidenuniv.nl>

Repository:

CRAN

Date/Publication:

2025-08-25 08:40:08 UTC

Standard Errors

Description

Returns the standard errors of the parameters of a fitted GPPM.

Usage

SE(object)

Arguments

object

object of class GPPM. Must be fitted, that is, a result from fit.GPPM.

Value

Standard errors for all parameters as a named numeric vector.

Examples


lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
lgcmFit <- fit(lgcm)
stdErrors <- SE(lgcmFit)

Accuracy Estimates for Predictions

Description

Estimate the accuracy based on predictions.

Usage

accuracy(predRes)

Arguments

predRes

object of class GPPMPred as obtained by predict.GPPM

Value

accuracy estimates in the form of the mean squared error (MSE), the negative log-predictive probability (nLPP), and the sum squared error (SSE)

Examples


data("demoLGCM")
# remove all measurements from person 1 and the first form person 2
predIdx <- c(which(demoLGCM$ID == 1), which(demoLGCM$ID == 2)[1])
fitDemoLGCM <- demoLGCM[setdiff(1:nrow(demoLGCM), predIdx), ]

lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  fitDemoLGCM, "ID", "y"
)
lgcm <- fit(lgcm)
predRes <- predict(lgcm, demoLGCM[predIdx, ])
accEsts <- accuracy(predRes)
accEsts$MSE # mean squared error
accEsts$nLPP # negative log-predictive probability
accEsts$MAE # mean absolute error

Point Estimates

Description

Extracts point estimates for all parameters from a fitted GPPM.

Usage

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

Arguments

object

object of class GPPM. Must be fitted, that is, a result from fit.GPPM.

...

additional arguments (currently not used).

Value

Point estimates for all parameters as a named numeric vector.

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
lgcmFit <- fit(lgcm)
paraEsts <- coef(lgcmFit)

Confidence Intervals

Description

Computes confidence intervals for one or more parameters in a fitted GPPM.

Usage

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

Arguments

object

object of class GPPM. Must be fitted, that is, a result from fit.GPPM.

parm

vector of strings. The parameters for which confidence intervals are desired. If missing, confidence intervals for all parameters are returned.

level

scalar from 0 to 1. The confidence level required.

...

additional arguments (currently not used).

Value

A matrix (or vector) with columns giving lower and upper confidence limits for each parameter. These will be labeled as (1-level)/2 and 1 - (1-level)/2 in \

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
lgcmFit <- fit(lgcm)
confInts <- confint(lgcmFit)

Covariance Function

Description

Extracts the covariance function from a GPPM.

Usage

covFun(gpModel)

Arguments

gpModel

object of class GPPM.

Value

The covariance function as a character string.

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
myCov <- covFun(lgcm)

Create Leave-persons-out Folds

Description

This function is used to create a leave-persons-out cross-validation fold vector to be used by crossvalidate.

Usage

createLeavePersonsOutFolds(gpModel, k = 10)

Arguments

gpModel

object of class GPPM.

k

integer scalar. Number of folds to create.

Details

The folds are created such that the data of each person is fully in one fold.

Value

A fold vector, which is a vector of length nrow(getData(gpModel)) of integers from 1 to k. If foldVector[i]=j, then data point i is assigned to fold j.

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
theFolds <- createLeavePersonsOutFolds(lgcm)

Cross-validation.

Description

Performs cross-validation of a Gaussian process panel model.

Usage

crossvalidate(gpModel, foldVector)

Arguments

gpModel

object of class GPPM.

foldVector

integer vector. Describes the foldstructure to use. For example, created by createLeavePersonsOutFolds.

Details

The fold vector, must be a vector of length nrow(getData(gpModel)) of integers from 1 to k. If foldVector[i]=j, then data point i is assigned to fold j.

Value

Cross-validation estimates of the mean squared error (MSE) and the negative log-predictive probability (nLPP)

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
theFolds <- createLeavePersonsOutFolds(lgcm, k = 2) # for speed, in practive rather use default k=10
crosRes <- crossvalidate(lgcm, theFolds)
crosRes$MSE # mean squared error
crosRes$nLPP # negative log-predictive probability

Simulated Data From a Latent Growth Curve Model.

Description

Simulated Data From a Latent Growth Curve Model.

Usage

demoLGCM

Format

A data frame with 1998 rows and 3 variables:

ID: Subject ID
t: Time index
y: Generic measurement

Generic Method For Fitting a model

Description

Generic method for fitting a model.

Usage

fit(gpModel, ...)

Arguments

gpModel

a model.

...

additional arguments.

Value

A fitted model

Fit a Gaussian process panel model

Description

This function is used to fit a Gaussian process panel model, which has been specified fit using gppm.

Usage

## S3 method for class 'GPPM'
fit(
  gpModel,
  init = "random",
  useOptimizer = TRUE,
  verbose = FALSE,
  hessian = TRUE,
  ...
)

Arguments

gpModel

object of class GPPM. The Gaussian process panel model to be fitted.

init

string or named numeric vector. Used to specify the starting values for the parameters. Can either be the string 'random' (default) or a numeric vector startVal of starting values. Which value belongs to which parameter is determined by the names attribute of startVal. See also the example.

useOptimizer

boolean. Should the optimizer be used or not? For false the (possibly random) starting values are returned as the maximum likelihood estimates.

verbose

boolean. Print diagnostic output?

hessian

boolean. Compute the hessian at the maximum likelihood estimate?

...

additional arguments (currently not used).

Value

A fitted Gaussian process panel model, which is an object of class 'GPPM'.

Examples


# regular usage
data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
lgcmFit <- fit(lgcm)

# starting values as ML results
startVals <- c(10, 1, 10, 3, 10, 1)
names(startVals) <- pars(lgcm)
lgcmFakeFit <- fit(lgcm, init = startVals, useOptimizer = FALSE)
stopifnot(identical(startVals, coef(lgcmFakeFit)))

Person-specific mean vectors and covariance matrices

Description

A fitted GPPM implies a mean vector and a covariance matrix for each person. These are returned by this function.

Usage

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

Arguments

object

object of class GPPM. Must be fitted, that is, a result from fit.GPPM.

...

additional arguments (currently not used).

Value

Returns a list structure with mean and covariances matrices. See example.

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
lgcmFit <- fit(lgcm)
meansCovs <- fitted(lgcmFit)

person1Mean <- meansCovs$mean[[1]]
person1Cov <- meansCovs$cov[[1]]
person1ID <- meansCovs$ID[[1]]

Data Set

Description

Extracts the data set from a GPPM.

Usage

getData(gpModel)

Arguments

gpModel

object of class GPPM.

Value

The data set associated with the GPPM.

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
myData <- getData(lgcm)

Generic Extraction Function

Description

Extracts internals from a GPPM.

Usage

getIntern(gpModel, quantity)

Arguments

gpModel

object of class GPPM.

quantity

character string. Name of the quantity to extract. Possible values are

"parsedmFormula" for the parsed mean formula
"parsedcFormula" for the parsed covariance formula
"stanData" for the data set in the form needed for rstan
"stanModel" for the created rstan model
"stanOut" for the created stan output

Value

The requested quantity

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
lgcmFit <- fit(lgcm)
getIntern(lgcmFit, "parsedmFormula")

Define a Gaussian process panel model

Description

This function is used to specify a Gaussian process panel model (GPPM), which can then be fit using fit.GPPM.

Usage

gppm(mFormula, cFormula, myData, ID, DV, control = gppmControl())

Arguments

mFormula

character string. Contains the specification of the mean function. See details for more information.

cFormula

character string. Contains the specification of the covariance function. See details for more information.

myData

data frame. Contains the data to which the model is fitted. Must be in the long-format.

ID

character string. Contains the column label in myData which describes the subject ID.

DV

character string. Contains the column label in myData which contains the to be modeled variable.

control

object of class GPPMControl. Used for storing technical settings. Default should only be changed by advanced users. Generated via gppmControl.

Details

mFormula and cFormula contain the specification of the mean and the covariance function respectively. These formulas are defined using character strings. Within these strings there are four basic elements:

Parameters
Functions and operators
References to observed variables in the data frame myData
Mathematical constants

The gppm function automatically recognizes which part of the string refers to which elements. To be able to do this certain relatively common rules need to be followed:

Parameters: Parameters may not have the same name as any of the columns in myData to avoid confusing them with a reference to an observed variable. Furthermore, to avoid confusing them with functions, operators, or constants, parameter labels must always begin with a lower case letter and only contain letters and digits.

Functions and operators: All functions and operators that are supported by stan can be used; see https://mc-stan.org/docs/ for a full list. In general, all basic operators and functions are supported.

References: A reference must be the same as one of the elements of the output of names(myData). For references, the same rules apply as for parameters. That is, the column names of myData may only contain letters and digits and must start with a letter.

Constants: Again, all constants that are supported by stan can be used and in general the constants are available by their usual name.

Value

A (unfitted) Gaussian process panel model, which is an object of class 'GPPM'

Examples

# Defintion of a latent growth curve model

data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)

Define settings for a Gaussian process panel model

Description

This function is used to specify the settings of a Gaussian process panel model generated by gppm.

Usage

gppmControl(stanModel = TRUE)

Arguments

stanModel

boolean. Should the corresponding stan model be created? Should only be set to FALSE for testing purposes. Not creating the stan model makes model fitting impossible but saves a lot of time.

Value

Settings for a Gaussian process panel model in an object of class 'GPPMControl'

Log-Likelihood

Description

Compute the log-likelihood for a GPPM at the maximum likelihood parameter values.

Usage

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

Arguments

object

object of class GPPM. Must be fitted, that is, a result from fit.GPPM.

...

additional arguments (currently not used).

Value

Returns an object of class logLik. Attributes are: "df" (degrees of freedom; number of estimated parameters in the model) and nobs (number of persons in the model)

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
lgcmFit <- fit(lgcm)
ll <- logLik(lgcmFit)

Maximum Number of Observations per Person

Description

Extracts the maximum number of observations per person from a GPPM.

Usage

maxNObs(gpModel)

Arguments

gpModel

object of class GPPM.

Value

Maximum number of observations as a numeric.

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
maxNumberObs <- maxNObs(lgcm)

Mean Function

Description

Extracts the mean function from a GPPM.

Usage

meanFun(gpModel)

Arguments

gpModel

object of class GPPM.

Value

The mean function as a character string.

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
myMean <- meanFun(lgcm)

Number of Observations

Description

Extracts the number of observations for each person from a GPPM.

Usage

nObs(gpModel)

Arguments

gpModel

object of class GPPM.

Value

Number of observations for each person as a numeric vector. The corresponding IDs are in the IDs attribute.

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
numberObs <- nObs(lgcm)

Number of Parameters

Description

Extracts the number of parameters from a GPPM.

Usage

nPars(gpModel)

Arguments

gpModel

object of class GPPM.

Value

Number of parameters as a numeric.

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
numberParas <- nPars(lgcm)

Number of persons

Description

Extracts the number of persons from a GPPM.

Usage

nPers(gpModel)

Arguments

gpModel

object of class GPPM.

Value

Number of persons as a numeric.

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
numberPersons <- nPers(lgcm)

Number of Predictors

Description

Extracts the number of predictors from a GPPM.

Usage

nPreds(gpModel)

Arguments

gpModel

object of class GPPM.

Value

Number of predictors as numeric.

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
numberPreds <- nPreds(lgcm)

Essential Parameter Estimation Results

Description

Extracts the essential parameter estimation results for a GPPM.

Usage

parEsts(object, level = 0.95)

Arguments

object

object of class GPPM. Must be fitted, that is, a result from fit.GPPM.

level

scalar from 0 to 1. The confidence level required.

Value

A data.frame containing the estimated parameters, standard errors, and the lower and upper bounds of the confidence intervals.

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
lgcmFit <- fit(lgcm)
paramEssentials <- parEsts(lgcmFit)

Parameter Names

Description

Extracts the parameter names from a GPPM.

Usage

pars(gpModel)

Arguments

gpModel

object of class GPPM.

Value

The names of the parameters

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
parameters <- pars(lgcm)

Plotting predictions

Description

Plots person-specific predictions

Usage

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

Arguments

x

object of class GPPMPred as obtained by predict.GPPM

plotId

character string or integer. ID of the person for which the predictions should be plotted

...

additional arguments (currently not used).

Value

A plot visualizing the predictive distribution. The bold line describes the mean and the shaded area the 95\

Examples


data("demoLGCM")
# remove all measurements from person 1 and the first form person 2
predIdx <- c(which(demoLGCM$ID == 1), which(demoLGCM$ID == 2)[1])
fitDemoLGCM <- demoLGCM[setdiff(1:nrow(demoLGCM), predIdx), ]

lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  fitDemoLGCM, "ID", "y"
)
lgcm <- fit(lgcm)
predRes <- predict(lgcm, demoLGCM[predIdx, ])
plot(predRes, 1)

Plot a Long Data Frame

Description

This function is used to plot data from class 'LongData' as it is returned by getData simulate.GPPM.

Usage

## S3 method for class 'LongData'
plot(x, plotIds, by, ID, DV, ...)

Arguments

x

longitudinal data frame of class 'LongData'.

plotIds

vector of IDs for which the data should be printed. Can be left empty. Then 5 IDs are picked randomly.

by

label of the variable on the x-axis. Can be left empty.

ID

label of the ID column. Can be left empty.

DV

label of the variable on the y-axis. Can be left empty.

...

additional parameters (currently not used).

Value

a fitted Gaussian process panel model, which is an object of class 'GPPM'

Examples

data("demoLGCM")
plot(demoLGCM, plotIds = c(1, 2, 3))
plot(demoLGCM) # five random ids

GPPM predictions

Description

Obtain person-specific predictions.

Usage

## S3 method for class 'GPPM'
predict(object, newData, ...)

Arguments

object

object of class GPPM. Must be fitted, that is, a result from fit.GPPM.

newData

a data frame with the same column names as the data frame used for generating gpModel with gppm. May only contain new data, that is, data that was not used for fitting.

...

additional arguments (currently not used).

Value

Predictions of the dependent variable for all rows in newData. Conditional predictions for all persons in newData that are also present in the data used for fitting gpModel; unconditional predictions for others persons. See examples for format.

Examples


data("demoLGCM")
# remove all measurements from person 1 and the first form person 2
predIdx <- c(which(demoLGCM$ID == 1), which(demoLGCM$ID == 2)[1])
fitDemoLGCM <- demoLGCM[setdiff(1:nrow(demoLGCM), predIdx), ]

lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  fitDemoLGCM, "ID", "y"
)
lgcm <- fit(lgcm)
predRes <- predict(lgcm, demoLGCM[predIdx, ])

Predictors Names

Description

Extracts the predictor names from a GPPM.

Usage

preds(gpModel)

Arguments

gpModel

object of class GPPM.

Value

The names of the predictors.

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
myPreds <- preds(lgcm)

Simulate from a Gaussian process panel model

Description

This function is used to simulate from a Gaussian process panel model, which has been specified using gppm.

Usage

## S3 method for class 'GPPM'
simulate(
  object,
  nsim = 1,
  seed = NULL,
  parameterValues = NULL,
  verbose = FALSE,
  ...
)

Arguments

object

object of class GPPM. The Gaussian process panel model from which to simulate.

nsim

integer. Number of data sets to generate.

seed

numeric. Random seed to be used.

parameterValues

numeric vector. Used to specify the values for the parameters. Which value belongs to which parameter is determined by the names attribute of parameterValues. See also the example.

verbose

boolean. Print diagnostic output?

...

additional parameters (currently not used).

Value

A simulated data set, which is an object of class 'LongData'. If nsim>1 a list of nsim simulated data sets.

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)

parameterValues <- c(10, -1, 0, 10, 0, 0.1)
names(parameterValues) <- c("muI", "muS", "varI", "varS", "covIS", "sigma")
simData <- simulate(lgcm, parameterValues = parameterValues)

Summarizing GPPM

Description

This function is used to summarize a GPPM. summary method for class 'GPPM'.

Usage

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

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

Arguments

object

object of class GPPM.

...

additional parameters (currently not used).

x

output of fit.GPPM

Value

An object of class "summary.GPPM", which is a list with 4 entries:

modelSpecification an object of class 'ModelSpecification' describing the model as a list with the following entries
- meanFormula formula for the mean function; output of meanFun
- covFormula formula for the covariance function; output of covFun
- nPars number of parameters; output of nPars
- params parameter names; output of pars
- nPreds number of predictors; output of nPreds
- preds predictors names; output of preds
parameterEstimates a data frame containing a summary of the parameter estimates; output of parEsts
modelfit An object of class "ModelFit" describing the modelfit using a list with the following entries
- AIC AIC of the model; output of AIC
- BIC BIC of the model; output of BIC
- logLik log-likelihood of the model; output of logLik
dataStats An object of class "DataStats" describing the data set using a list with the following entries
- nPer number of persons; output of nPers
- maxTime maximum number of observations per person; output of maxNObs
- nTime number of observations for each person; output of nObs

Methods (by generic)

print(summary.GPPM): Printing a summary.GPPM object

Parameters used for generating `demoLGCM`.

Description

Parameters used for generating demoLGCM.

Usage

trueParas

Format

A parameter vector.

Variance-Covariance Matrix

Description

Returns the variance-covariance matrix of the parameters of a fitted GPPM.

Usage

## S3 method for class 'GPPM'
vcov(object, ...)

Arguments

object

object of class GPPM. Must be fitted, that is, a result from fit.GPPM.

...

additional arguments (currently not used).

Value

A matrix of the estimated covariances between the parameter estimates. This has row and column names corresponding to the parameter names.

Examples


data("demoLGCM")
lgcm <- gppm(
  "muI+muS*t", "varI+covIS*(t+t#)+varS*t*t#+(t==t#)*sigma",
  demoLGCM, "ID", "y"
)
lgcmFit <- fit(lgcm)
covMat <- vcov(lgcmFit)

Standard Errors

Description

Usage

Arguments

Value

See Also

Examples

Accuracy Estimates for Predictions

Description

Usage

Arguments

Value

Examples

Point Estimates

Description

Usage

Arguments

Value

See Also

Examples

Confidence Intervals

Description

Usage

Arguments

Value

See Also

Examples

Covariance Function

Description

Usage

Arguments

Value

See Also

Examples

Create Leave-persons-out Folds

Description

Usage

Arguments

Details

Value

See Also

Examples

Cross-validation.

Description

Usage

Arguments

Details

Value

Examples

Simulated Data From a Latent Growth Curve Model.

Description

Usage

Format

Generic Method For Fitting a model

Description

Usage

Arguments

Value

See Also

Fit a Gaussian process panel model

Description

Usage

Arguments

Value

See Also

Examples

Person-specific mean vectors and covariance matrices

Description

Usage

Arguments

Value

See Also

Examples

Data Set

Description

Usage

Arguments

Value

See Also

Examples