PLmixed: Fit GLMM with Factor Structure
In PLmixed: Estimate (Generalized) Linear Mixed Models with Factor Structures
View source: R/PLmixed_main_function.R
PLmixed R Documentation
Fit GLMM with Factor Structure
Description
Fit a (generalized) linear mixed effects model (GLMM) with factor structures. Utilizes both the
lme4 package and optim function for estimation using a profile-likelihood based
approach.
Usage
PLmixed(
formula,
data,
family = gaussian,
load.var = NULL,
lambda = NULL,
factor = NULL,
init = 1,
nlp = NULL,
init.nlp = 1,
nAGQ = 1,
method = "L-BFGS-B",
lower = -Inf,
upper = Inf,
lme4.optimizer = "bobyqa",
lme4.start = NULL,
lme4.optCtrl = list(),
opt.control = NULL,
REML = FALSE,
SE = 1,
ND.method = "simple",
check = "stop",
est = TRUE,
iter.count = TRUE
)
Arguments
formula
A formula following that of lme4, with the addition that factors can be specified
as random effects. Factor names should not be names of variables in the data set, and are instead
defined with the factor argument.
data
A data frame containing the variables used in the model (but not factor names).
family
A GLM family, see glm and family.
load.var
A variable in the dataframe identifying what the factors load onto. Each unique element in load.var will have
a unique factor loading. All rows in the dataset with the same value for load.var will have the same factor loading.
lambda
A matrix or list of matrices corresponding to the loading matrices. A value of NA
indicates the loading is freely estimated, while a numeric entry indicates a constraint.
factor
A list of factors corresponding to the loading matrices and factors specified in model.
init
A scalar (default = 1) or vector of initial lambda values. If a scalar, the value is applied to all lambda parameters.
If a vector, the values apply in row by column by matrix order.
nlp
A character vector containing the names of additional nonlinear parameters that are in the model formula.
init.nlp
A scalar (default = 1) or vector of initial nlp values. If a scalar, the value is applied to all nlp parameters.
If a vector, the values apply in the order listed.
nAGQ
If family is non-gaussian, the number of points per axis for evaluating the adaptive
Gauss-Hermite approximation to the log-likelihood. Defaults to 1, corresponding to the Laplace approximation.
See glmer.
method
The optimx optimization method. Defaults to L-BFGS-B.
lower
Lower bound on lambda parameters if applicable.
upper
Upper bound on lambda parameters if applicable.
lme4.optimizer
The lme4 optimization method.
lme4.start
Start values used for lme4.
lme4.optCtrl
A list controlling the lme4 optimization. See lmerControl
or glmerControl
opt.control
Controls for the optimx optimization.
REML
Use REML if model is linear? Defaults to FALSE.
SE
Method of calculating standard errors for fixed effects.
ND.method
Method of calculating numerical derivatives.
check
Check number of observations vs. levels and number of observations vd. random effects.
est
Return parameter estimates.
iter.count
Print the iteration counter during optimization.
Details
Factors are listed within the formula in the same way that random effects are specified
in lme4. The grouping variable listed after | defines what the factor values randomly
vary over, just as | does for other random effects. The names of factors and other random
effect terms can be listed within the same set of parentheses, allowing the covariance between the
factor(s) and random effect(s) to be estimated. The same factor may be specified for multiple grouping
variables, allowing for multilevel or crossed effects.
The factor argument must list any factor that appears in the formula. The ordering will
depend on the ordering of the matrices listed within lambda. The matrices in lambda
specify the factor loading matrices. The number of matrices in lambda should equal the number
of character vectors in factor and the number of elements in load.var. The number of
rows in the kth matrix listed in lambda should correspond to the number of unique elements
in the dataset for the kth variable listed in load.var, and the number of columns in the kth
matrix should correspond to the number of factors listed in the kth character vector of factor.
Within the kth matrix, the (i, j) cell corresponds to the factor loading for the ith unique element
of the kth variable listed in load.var on the jth factor listed in the kth character vector
of factor. Each element of the matrix should be either a number or NA. If the element is a
number, the loading will be constrained to that value. If the element is an NA, the loading will
be freely estimated. For identification, it is necessary (but not sufficient) for at least one element in
each column to be constrained.
The nlp argument can be viewed as a special case of the factor argument, where the character vector
listed in nlp is automatically linked to 1 x p lambda matrix, where p is the number of elements in nlp.
The load.var for these parameters is viewed as a constant, so that the nlp parameters are equivalent for
all rows in the dataset. Thus, nlp simplifies the process of adding additional nonlinear parameters to the model
without having to specify corresponding lambda and load.var values.
Value
An object of class PLmod, which contains an object of class merMod as one of its elements.
Some functions for class merMod have been adapted to work with class PLmod. Others can be utilized
using object$'lme4 Model', where object is an object of class PLmod.
References
Rockwood, N. J., & Jeon, M. (2019). Estimating complex measurement and growth models
using the R package PLmixed.Multivariate Behavioral Research, 54(2), 288-306.
Jeon, M., & Rabe-Hesketh, S. (2012). Profile-likelihood approach for estimating
generalized linear mixed models with factor structures. Journal of Educational
and Behavioral Statistics, 37(4), 518-542.
See Also
lme4
glmer
lmer
Examples
data("IRTsim") # Load the IRTsim data
IRTsub <- IRTsim[IRTsim$item < 4, ] # Select items 1-3
set.seed(12345)
IRTsub <- IRTsub[sample(nrow(IRTsub), 300), ] # Randomly sample 300 responses
IRTsub <- IRTsub[order(IRTsub$item), ] # Order by item
irt.lam = c(1, NA, NA) # Specify the lambda matrix
# Below, the # in front of family = binomial can be removed to change the response distribution
# to binomial, where the default link function is logit.
irt.model <- PLmixed(y ~ 0 + as.factor(item) + (0 + abil.sid |sid) +(0 + abil.sid |school),
data = IRTsub, load.var = c("item"), # family = binomial,
factor = list(c("abil.sid")), lambda = list(irt.lam))
summary(irt.model)
## Not run:
# A more time-consuming example.
# ~ 5-10 minutes
data("KYPSsim") # Load the KYPSsim data
kyps.lam <- rbind(c( 1, 0), # Specify the lambda matrix
c(NA, 0),
c(NA, 1),
c(NA, NA))
kyps.model <- PLmixed(esteem ~ as.factor(time) + (0 + hs | hid)
+ (0 + ms | mid) + (1 | sid), data = KYPSsim,
factor = list(c("ms", "hs")), load.var = c("time"),
lambda = list(kyps.lam))
summary(kyps.model)
data("JUDGEsim")
JUDGEsim <- JUDGEsim[order(JUDGEsim$item), ] # Order by item
unique(JUDGEsim$item)
# Specify Lambda matrix
judge.lam <- rbind(c( 1, 0, 1, 0, 0, 0),
c(NA, 0, NA, 0, 0, 0),
c(NA, 0, NA, 0, 0, 0),
c( 0, 1, 0, 1, 0, 0),
c( 0, NA, 0, NA, 0, 0),
c( 0, NA, 0, NA, 0, 0),
c( 0, 0, 0, 0, 1, 0),
c( 0, 0, 0, 0, NA, 0),
c( 0, 0, 0, 0, NA, 0),
c( 0, 0, 0, 0, 0, 1),
c( 0, 0, 0, 0, 0, NA),
c( 0, 0, 0, 0, 0, NA))
# Conduct analysis
judge.example <- PLmixed(response ~ 0 + as.factor(item) + (1 | class)
+ (0 + trait1.t + trait2.t + trait1.s + trait2.s | stu)
+ (0 + teacher1 + teacher2 | tch), data = JUDGEsim,
lambda = list(judge.lam), load.var = "item",
factor = list(c("teacher1", "teacher2", "trait1.t",
"trait2.t", "trait1.s", "trait2.s")))
summary(judge.example)
data("KYPSitemsim")
time.lam <- rbind(c( 1, 0), # Specify time lambda matrix
c(NA, 0),
c(NA, 1),
c(NA, NA))
item.lam <- c(1, NA, NA, NA, NA, NA) # Specify item lambda matrix
KYPSitemsim$time2 <- (KYPSitemsim$time == 2) * 1
KYPSitemsim$time3 <- (KYPSitemsim$time == 3) * 1
KYPSitemsim$time4 <- (KYPSitemsim$time == 4) * 1
kyps.item.model <- PLmixed(response ~ 0 + as.factor(item) + lat.var:time2
+ lat.var:time3 + lat.var:time4 + (0 + hs:lat.var | hid)
+ (0 + ms:lat.var | mid) + (0 + lat.var:as.factor(time) | id),
data = KYPSitemsim, lambda = list(time.lam, item.lam),
factor = list(c("ms", "hs"), "lat.var"),
load.var = c("time", "item"))
summary(kyps.item.model)
## End(Not run)
PLmixed documentation built on Aug. 24, 2023, 1:09 a.m.
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View source: R/PLmixed_main_function.R
| PLmixed | R Documentation |
Fit GLMM with Factor Structure
Description
Fit a (generalized) linear mixed effects model (GLMM) with factor structures. Utilizes both the
lme4 package and optim function for estimation using a profile-likelihood based
approach.
Usage
PLmixed(
formula,
data,
family = gaussian,
load.var = NULL,
lambda = NULL,
factor = NULL,
init = 1,
nlp = NULL,
init.nlp = 1,
nAGQ = 1,
method = "L-BFGS-B",
lower = -Inf,
upper = Inf,
lme4.optimizer = "bobyqa",
lme4.start = NULL,
lme4.optCtrl = list(),
opt.control = NULL,
REML = FALSE,
SE = 1,
ND.method = "simple",
check = "stop",
est = TRUE,
iter.count = TRUE
)
Arguments
formula |
A formula following that of lme4, with the addition that factors can be specified
as random effects. Factor names should not be names of variables in the data set, and are instead
defined with the |
data |
A data frame containing the variables used in the model (but not factor names). |
family |
A GLM family, see |
load.var |
A variable in the dataframe identifying what the factors load onto. Each unique element in |
lambda |
A matrix or list of matrices corresponding to the loading matrices. A value of NA indicates the loading is freely estimated, while a numeric entry indicates a constraint. |
factor |
A list of factors corresponding to the loading matrices and factors specified in model. |
init |
A scalar (default = |
nlp |
A character vector containing the names of additional nonlinear parameters that are in the model formula. |
init.nlp |
A scalar (default = |
nAGQ |
If family is non-gaussian, the number of points per axis for evaluating the adaptive
Gauss-Hermite approximation to the log-likelihood. Defaults to |
method |
The |
lower |
Lower bound on lambda parameters if applicable. |
upper |
Upper bound on lambda parameters if applicable. |
lme4.optimizer |
The lme4 optimization method. |
lme4.start |
Start values used for lme4. |
lme4.optCtrl |
A list controlling the lme4 optimization. See |
opt.control |
Controls for the |
REML |
Use REML if model is linear? Defaults to |
SE |
Method of calculating standard errors for fixed effects. |
ND.method |
Method of calculating numerical derivatives. |
check |
Check number of observations vs. levels and number of observations vd. random effects. |
est |
Return parameter estimates. |
iter.count |
Print the iteration counter during optimization. |
Details
Factors are listed within the formula in the same way that random effects are specified
in lme4. The grouping variable listed after | defines what the factor values randomly
vary over, just as | does for other random effects. The names of factors and other random
effect terms can be listed within the same set of parentheses, allowing the covariance between the
factor(s) and random effect(s) to be estimated. The same factor may be specified for multiple grouping
variables, allowing for multilevel or crossed effects.
The factor argument must list any factor that appears in the formula. The ordering will
depend on the ordering of the matrices listed within lambda. The matrices in lambda
specify the factor loading matrices. The number of matrices in lambda should equal the number
of character vectors in factor and the number of elements in load.var. The number of
rows in the kth matrix listed in lambda should correspond to the number of unique elements
in the dataset for the kth variable listed in load.var, and the number of columns in the kth
matrix should correspond to the number of factors listed in the kth character vector of factor.
Within the kth matrix, the (i, j) cell corresponds to the factor loading for the ith unique element
of the kth variable listed in load.var on the jth factor listed in the kth character vector
of factor. Each element of the matrix should be either a number or NA. If the element is a
number, the loading will be constrained to that value. If the element is an NA, the loading will
be freely estimated. For identification, it is necessary (but not sufficient) for at least one element in
each column to be constrained.
The nlp argument can be viewed as a special case of the factor argument, where the character vector
listed in nlp is automatically linked to 1 x p lambda matrix, where p is the number of elements in nlp.
The load.var for these parameters is viewed as a constant, so that the nlp parameters are equivalent for
all rows in the dataset. Thus, nlp simplifies the process of adding additional nonlinear parameters to the model
without having to specify corresponding lambda and load.var values.
Value
An object of class PLmod, which contains an object of class merMod as one of its elements.
Some functions for class merMod have been adapted to work with class PLmod. Others can be utilized
using object$'lme4 Model', where object is an object of class PLmod.
References
Rockwood, N. J., & Jeon, M. (2019). Estimating complex measurement and growth models using the R package PLmixed.Multivariate Behavioral Research, 54(2), 288-306.
Jeon, M., & Rabe-Hesketh, S. (2012). Profile-likelihood approach for estimating generalized linear mixed models with factor structures. Journal of Educational and Behavioral Statistics, 37(4), 518-542.
See Also
lme4
glmer
lmer
Examples
data("IRTsim") # Load the IRTsim data
IRTsub <- IRTsim[IRTsim$item < 4, ] # Select items 1-3
set.seed(12345)
IRTsub <- IRTsub[sample(nrow(IRTsub), 300), ] # Randomly sample 300 responses
IRTsub <- IRTsub[order(IRTsub$item), ] # Order by item
irt.lam = c(1, NA, NA) # Specify the lambda matrix
# Below, the # in front of family = binomial can be removed to change the response distribution
# to binomial, where the default link function is logit.
irt.model <- PLmixed(y ~ 0 + as.factor(item) + (0 + abil.sid |sid) +(0 + abil.sid |school),
data = IRTsub, load.var = c("item"), # family = binomial,
factor = list(c("abil.sid")), lambda = list(irt.lam))
summary(irt.model)
## Not run:
# A more time-consuming example.
# ~ 5-10 minutes
data("KYPSsim") # Load the KYPSsim data
kyps.lam <- rbind(c( 1, 0), # Specify the lambda matrix
c(NA, 0),
c(NA, 1),
c(NA, NA))
kyps.model <- PLmixed(esteem ~ as.factor(time) + (0 + hs | hid)
+ (0 + ms | mid) + (1 | sid), data = KYPSsim,
factor = list(c("ms", "hs")), load.var = c("time"),
lambda = list(kyps.lam))
summary(kyps.model)
data("JUDGEsim")
JUDGEsim <- JUDGEsim[order(JUDGEsim$item), ] # Order by item
unique(JUDGEsim$item)
# Specify Lambda matrix
judge.lam <- rbind(c( 1, 0, 1, 0, 0, 0),
c(NA, 0, NA, 0, 0, 0),
c(NA, 0, NA, 0, 0, 0),
c( 0, 1, 0, 1, 0, 0),
c( 0, NA, 0, NA, 0, 0),
c( 0, NA, 0, NA, 0, 0),
c( 0, 0, 0, 0, 1, 0),
c( 0, 0, 0, 0, NA, 0),
c( 0, 0, 0, 0, NA, 0),
c( 0, 0, 0, 0, 0, 1),
c( 0, 0, 0, 0, 0, NA),
c( 0, 0, 0, 0, 0, NA))
# Conduct analysis
judge.example <- PLmixed(response ~ 0 + as.factor(item) + (1 | class)
+ (0 + trait1.t + trait2.t + trait1.s + trait2.s | stu)
+ (0 + teacher1 + teacher2 | tch), data = JUDGEsim,
lambda = list(judge.lam), load.var = "item",
factor = list(c("teacher1", "teacher2", "trait1.t",
"trait2.t", "trait1.s", "trait2.s")))
summary(judge.example)
data("KYPSitemsim")
time.lam <- rbind(c( 1, 0), # Specify time lambda matrix
c(NA, 0),
c(NA, 1),
c(NA, NA))
item.lam <- c(1, NA, NA, NA, NA, NA) # Specify item lambda matrix
KYPSitemsim$time2 <- (KYPSitemsim$time == 2) * 1
KYPSitemsim$time3 <- (KYPSitemsim$time == 3) * 1
KYPSitemsim$time4 <- (KYPSitemsim$time == 4) * 1
kyps.item.model <- PLmixed(response ~ 0 + as.factor(item) + lat.var:time2
+ lat.var:time3 + lat.var:time4 + (0 + hs:lat.var | hid)
+ (0 + ms:lat.var | mid) + (0 + lat.var:as.factor(time) | id),
data = KYPSitemsim, lambda = list(time.lam, item.lam),
factor = list(c("ms", "hs"), "lat.var"),
load.var = c("time", "item"))
summary(kyps.item.model)
## End(Not run)
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