mirt (version 0.8.0)

multipleGroup: Multiple Group Estimation

Description

multipleGroup performs a full-information maximum-likelihood multiple group analysis for dichotomous and polytomous data under the item response theory paradigm using either Cai's (2010) Metropolis-Hastings Robbins-Monro (MHRM) algorithm or with an EM algorithm approach.

Usage

multipleGroup(data, model, group, itemtype = NULL, guess
    = 0, upper = 1, SE = FALSE, SE.type = 'SEM', invariance
    = '', pars = NULL, method = 'EM', constrain = NULL,
    parprior = NULL, calcNull = TRUE, draws = 5000, quadpts
    = NULL, grsm.block = NULL, rsm.block = NULL, key =
    NULL, cl = NULL, technical = list(), verbose = TRUE,
    ...)

  ## S3 method for class 'MultipleGroupClass':
coef(object, digits = 3,
    verbose = TRUE, ...)

  ## S3 method for class 'MultipleGroupClass':
summary(object, digits =
    3, verbose = TRUE, ...)

  ## S3 method for class 'MultipleGroupClass':
anova(object, object2)

  ## S3 method for class 'MultipleGroupClass':
residuals(object, ...)

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

  ## S3 method for class 'MultipleGroupClass':
plot(x, y, type = 'info',
    npts = 50, theta_angle = 45, rot = list(xaxis = -70,
    yaxis = 30, zaxis = 10), ...)

Arguments

data

a matrix or data.frame that consists of numerically ordered data, with missing data coded as NA

model

an object or named list of objects returned from confmirt.model() declaring how the factor model is to be estimated. The names of the list input must correspond to the unique values in the group variable. See

group

a character vector indicating group membership

invariance

a character vector containing the following possible options: [object Object],[object Object],[object Object],[object Object],[object Object] Additionally, specifying specific item name bundles (from colnames(data)) will constrain

guess

initial (or fixed) values for the pseudo-guessing parameter. Can be entered as a single value to assign a global guessing parameter or may be entered as a numeric vector for each item

upper

initial (or fixed) upper bound parameters for 4-PL model. Can be entered as a single value to assign a global upper bound parameter or may be entered as a numeric vector corresponding to each item

SE

logical; estimate the information matrix for standard errors?

SE.type

see mirt for more details

verbose

logical; display iteration history during estimation?

draws

the number of Monte Carlo draws to estimate the log-likelihood

quadpts

the number of quadratures to be used per dimensions when method = 'EM'

calcNull

logical; calculate the Null model for fit statics (e.g., TLI)?

cl

a cluster object from the parallel package

method

a character indicating whether to use the EM ('EM') or the MH-RM ('MHRM') algorithm

type

type of plot to view; can be 'info' to show the test information function, 'infocontour' for the test information contours, 'SE' for the test standard error function, 'RE' for the relative ef

theta_angle

numeric values ranging from 0 to 90 used in plot

npts

number of quadrature points to be used for plotting features. Larger values make plots look smoother

rot

allows rotation of the 3D graphics

x

an object of class mirt to be plotted or printed

y

an unused variable to be ignored

key

see mirt for details

itemtype

see mirt for details

constrain

see mirt for details

grsm.block

see mirt for details

rsm.block

see mirt for details

parprior

see mirt for details

pars

see mirt for details

object

an object of class confmirtClass

object2

an object of class confmirtClass

digits

the number of significant digits to be rounded

...

additional arguments to be passed

technical

list specifying subtle parameters that can be adjusted. These values are [object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Details

By default the estimation in multipleGroup assumes that the models are maximally independent, and therefore could initially be performed by sub-setting the data and running identical models with confmirt or mirt and aggregating the results (e.g., log-likelihood). However, constrains may be imposed across groups by invoking various invariance keywords and constrain = ... arguments, by inputting user specified design matrix from mod2values or from passing pars = 'values', or by supplying a constrain list for user defined equality constraints between parameters.

See Also

expand.table, key2binary, confmirt.model, mirt, confmirt, bfactor, multipleGroup, mixedmirt, wald, itemplot, fscores, fitIndices, extract.item, iteminfo, testinfo, probtrace, boot.mirt, imputeMissing, itemfit, mod2values, read.mirt, simdata, createItem

Examples

#single factor
set.seed(12345)
a <- matrix(abs(rnorm(15,1,.3)), ncol=1)
d <- matrix(rnorm(15,0,.7),ncol=1)
itemtype <- rep('dich', nrow(a))
N <- 1000
dataset1 <- simdata(a, d, N, itemtype)
dataset2 <- simdata(a, d, N, itemtype, mu = .1, sigma = matrix(1.5))
dat <- rbind(dataset1, dataset2)
group <- c(rep('D1', N), rep('D2', N))
models <- confmirt.model('F1 = 1-15')

mod_configural <- multipleGroup(dat, models, group = group) #completely separate analyses

# prev.mod can save precious iterations and help to avoid local minimums
mod_metric <- multipleGroup(dat, models, group = group, invariance=c('slopes')) #equal slopes
#equal intercepts, free variance and means
mod_scalar2 <- multipleGroup(dat, models, group = group,
                             invariance=c('slopes', 'intercepts', 'free_varcov','free_means'))
mod_scalar1 <- multipleGroup(dat, models, group = group,  #fixed means
                             invariance=c('slopes', 'intercepts', 'free_varcov'))
mod_fullconstrain <- multipleGroup(dat, models, group = group,
                             invariance=c('slopes', 'intercepts'))

summary(mod_scalar2)
coef(mod_scalar2)
residuals(mod_scalar2)
plot(mod_configural)
plot(mod_configural, type = 'score')
itemplot(mod_configural, 2)
itemplot(mod_configural, 2, type = 'RE')

anova(mod_metric, mod_configural) #equal slopes only
anova(mod_scalar2, mod_metric) #equal intercepts, free variance and mean
anova(mod_scalar1, mod_scalar2) #fix mean
anova(mod_fullconstrain, mod_scalar1) #fix variance


#test whether first 6 slopes should be equal across groups
values <- multipleGroup(dat, models, group = group, pars = 'values')
values
constrain <- list(c(1, 63), c(5,67), c(9,71), c(13,75), c(17,79), c(21,83))
equalslopes <- multipleGroup(dat, models, group = group, constrain = constrain)
anova(equalslopes, mod_configural)

#############
#DIF test for each item (using all other items as anchors)
itemnames <- colnames(dat)
refmodel <- multipleGroup(dat, models, group = group,
                             invariance=c('free_means', 'free_varcov', itemnames))

#loop over items (in practice, run in parallel to increase speed)
estmodels <- vector('list', ncol(dat))
for(i in 1:ncol(dat))
    estmodels[[i]] <- multipleGroup(dat, models, group = group, verbose = FALSE,
                             invariance=c('free_means', 'free_varcov', itemnames[-i]))

(anovas <- lapply(estmodels, anova, object2=refmodel))

#family-wise error control
p <- do.call(rbind, lapply(anovas, function(x) x[2,9]))
p.adjust(p, method = 'BH')

#same as above, except only test if slopes vary (1 df)
#constrain all intercepts
estmodels <- vector('list', ncol(dat))
for(i in 1:ncol(dat))
    estmodels[[i]] <- multipleGroup(dat, models, group = group, verbose = FALSE,
                             invariance=c('free_means', 'free_varcov', 'intercepts',
                             itemnames[-i]))


(anovas <- lapply(estmodels, anova, object2=refmodel))

#############
#multiple factors

a <- matrix(c(abs(rnorm(5,1,.3)), rep(0,15),abs(rnorm(5,1,.3)),
rep(0,15),abs(rnorm(5,1,.3))), 15, 3)
d <- matrix(rnorm(15,0,.7),ncol=1)
mu <- c(-.4, -.7, .1)
sigma <- matrix(c(1.21,.297,1.232,.297,.81,.252,1.232,.252,1.96),3,3)
itemtype <- rep('dich', nrow(a))
N <- 1000
dataset1 <- simdata(a, d, N, itemtype)
dataset2 <- simdata(a, d, N, itemtype, mu = mu, sigma = sigma)
dat <- rbind(dataset1, dataset2)
group <- c(rep('D1', N), rep('D2', N))

#group models
model <- confmirt.model()
   F1 = 1-5
   F2 = 6-10
   F3 = 11-15

models <- list(D1=model, D2=model) #note the names match the groups

#EM approach (not as accurate with 3 factors, but generally good for quick model comparisons)
mod_configural <- multipleGroup(dat, models, group = group) #completely separate analyses
mod_metric <- multipleGroup(dat, models, group = group, invariance=c('slopes')) #equal slopes
mod_scalar <- multipleGroup(dat, models, group = group, #equal means, slopes, intercepts
                             invariance=c('slopes', 'intercepts', 'free_varcov'))
mod_fullconstrain <- multipleGroup(dat, models, group = group, #equal means, slopes, intercepts
                             invariance=c('slopes', 'intercepts'))

anova(mod_metric, mod_configural)
anova(mod_scalar, mod_metric)
anova(mod_fullconstrain, mod_scalar)

#same as above, but with MHRM (more accurate with 3 factors, but slower)
#completely separate analyses
mod_configural <- multipleGroup(dat, models, group = group, method = 'MHRM')
#equal slopes
mod_metric <- multipleGroup(dat, models, group = group, invariance=c('slopes'), method = 'MHRM')
#equal means, slopes, intercepts
mod_scalar <- multipleGroup(dat, models, group = group, method = 'MHRM',
                             invariance=c('slopes', 'intercepts', 'free_varcov'))
#equal means, slopes, intercepts
mod_fullconstrain <- multipleGroup(dat, models, group = group, method = 'MHRM',
                             invariance=c('slopes', 'intercepts'))

anova(mod_metric, mod_configural)
anova(mod_scalar, mod_metric)
anova(mod_fullconstrain, mod_scalar)

############
#polytomous item example
set.seed(12345)
a <- matrix(abs(rnorm(15,1,.3)), ncol=1)
d <- matrix(rnorm(15,0,.7),ncol=1)
d <- cbind(d, d-1, d-2)
itemtype <- rep('graded', nrow(a))
N <- 1000
dataset1 <- simdata(a, d, N, itemtype)
dataset2 <- simdata(a, d, N, itemtype, mu = .1, sigma = matrix(1.5))
dat <- rbind(dataset1, dataset2)
group <- c(rep('D1', N), rep('D2', N))
models <- confmirt.model('F1 = 1-15')
models2 <- confmirt.model('
   F1 = 1-10
   F2 = 10-15')

mod_configural <- multipleGroup(dat, models, group = group)
plot(mod_configural)
plot(mod_configural, type = 'SE')
itemplot(mod_configural, 1)
itemplot(mod_configural, 1, type = 'info')
fs <- fscores(mod_configural)
head(fs[["D1"]])
fscores(mod_configural, method = 'EAPsum')

mod_configural2 <- multipleGroup(dat, models2, group = group)
plot(mod_configural2, type = 'infocontour')
plot(mod_configural2, type = 'SE')
plot(mod_configural2, type = 'RE')
itemplot(mod_configural2, 10)