fit_irtree: Fit an mpt2irt model

In hplieninger/mpt2irt: Bringing Multinomial Processing Tree Models To Item Response Theory To Investigate Response Styles

Description

This function fits an mpt2irt model. Either the so-called Boeckenholt Model can be fit (fitModel = "2012") that assumes the three processes MRS, ERS, and target trait; or the so-called Acquiescence Model can be fit that additionally takes ARS into account (fitModel = "ext").

Usage

fit_irtree(X, revItem = NULL, traitItem = rep(1, ncol(X)), df = NULL,
  V = NULL, fitModel = c("ext", "2012", "pcm", "steps", "shift",
  "ext2"), model = NULL, fitMethod = c("stan", "jags"),
  outFormat = NULL, startSmall = FALSE, M = 1000, warmup = 1000,
  n.chains = 2, thin = 1, method = "parallel", add2varlist = NULL,
  cores = NULL, summarise = FALSE, N2 = 2, ...)

Arguments

X	an N x J matrix of observed responses for categories 1...5 (use mult_to_cat to transform a multinomial frequency matrix with 1s/0s to responses from 1...5)
revItem	vector of length J specifying reversed items (1=reversed, 0=regular)
traitItem	vector of length J specifying the underlying traits (e.g., indexed from 1...5). Standard: only a single trait is measured by all items. If the Big5 are measured, might be something like c(1,1,1,2,2,2,...,5,5,5,5)
df	degrees of freedom for wishart prior on covariance of traits (default: number of processes + 1)
V	prior for wishart distribution (default: diagonal matrix)
fitModel	Character. Either "2012" (Boeckenholt Model without acquiescence) or "ext" (Acquiescence Model). Details about all implemented models are described in the section Models below.
model	If NULL (the usual case), this is determined by fitModel. Otherwise, this is passed to sampling (for Stan) or run.jags (for JAGS).
fitMethod	whether to use JAGS or Stan
outFormat	either "mcmc.list" (can be analyzed with coda package) or "stan" or "runjags"
startSmall	Whether to use random starting values for beta sampled from "wide" (FALSE) or "narrow" priors (TRUE; beta and theta closer to 0; might solve problems with slow convergence of some chains for extreme starting values).
M	number of MCMC samples (after warmup)
warmup	number of samples for warmup (in JAGS: 1/5 for adaptation, 4/5 for burnin)
n.chains	number of MCMC chains (and number of CPUs used)
thin	thinning of MCMC samples
method	Passed to run.jags. Can be, for example, parallel or simple.
add2varlist	Additional variables to monitor (e.g., c("deviance", "pd", "popt", "dic") for JAGS)
cores	Passed to sampling: Number of cores to use when executing the chains in parallel.
summarise	Passed to run.jags: Should summary statistics be automatically calculated for the output chains? Defaults to FALSE, summaries can be calculated using tidyup_irtree_fit.
N2	Numeric. Number of persons for whom to draw posterior predictives. Specify equal to nrow(X) in order to draw values for all persons. This is mainly implemented for efficiency reasons in order to avoid massivly drawing samples which the user is not interested in.
...	further arguments passed to sampling (for Stan) or run.jags (for JAGS)

Details

Note that DIC can only be saved using fitMethod = "jags" in combination with method = "simple". Furthermore, you need to explicitly request DIC using, for example, add2varlist = c("deviance", "pd", "popt", "dic").

Value

Returns a list where the output from either JAGS or Stan is stored in the entry samples.

Models

The following models are currently implemented:

2012

This is the response style model proposed by Boeckenholt (2012) with parameters m (MRS), e (ERS), and t (target trait).

ext

This is the Acquiescence Model proposed by Plieninger and Heck (2018) with parameters m (MRS), e (ERS), a (ARS), and t (target trait). The e* parameter is constrained, namely, all item parameters are constrained to be equal.

steps

This is an ordinal IRT model without response styles as proposed by Tutz (1990) and Verhelst et al. (1997). It is also based on a tree structure but has only the parameter t (target trait).

pcm

This is an ordinal IRT model without response styles, namely, the partial credit model, which has only the parameter t (target trait).

shift

This is the tree-shift model proposed by Plieninger and Heck (2018) in Appendix A with parameters m (MRS), e (ERS), and ta (target trait and ARS). For regular items, ta = t + a, whereas for reversed items, ta = -t + a. Unlike the Acquiescence Model (ext), this model is not a mixture model.

ext2

This is the unrestricted version of the Acquiescence Model. Therein, fewer constraints are imposed on the e* parameter, and all its item parameters are free to vary.

Note on Output

In the output, the estimated parameters are always arranged in the order MRS, ERS, ARS, target trait(s). For example, a 2012-model with two target traits (specified via traitItem), has four person parameters and MRS is the first, ERS the second, and the two target traits the third and fourth.

Furthermore, only one subscript and column is used for each type of item parameter. That is, all β_t (i.e., target-trait difficulites) are stored in one column and traitItem indicates which parameter pertains to which target trait.

This is illustrated for two models in the following:

• Model 2012 (S = 2 + number of traits):

  • theta[i, 1:S] = c(MRS, ERS, target trait(s))

  • beta[j, 1:3] = c(MRS, ERS, target trait)

• Model ext (S = 3 + number of traits):

  • theta[i, 1:S] = c(MRS, ERS, ARS, target trait(s))

  • beta[j, 1:4] = c(MRS, ERS, ARS, target trait)

Examples

## Not run: 
N <- 20
J <- 10
betas <- cbind(rnorm(J, .5), rnorm(J, .5), rnorm(J, 1.5), rnorm(J, 0))
dat <- generate_irtree_ext(N = N, J = J, betas = betas, beta_ARS_extreme = .5)

# fit model
res1 <- fit_irtree(dat$X, revItem = dat$revItem, M = 200)
res2 <- summarize_irtree_fit(res1)
res3 <- tidyup_irtree_fit(res2)
names(res3)
res3$plot

## End(Not run)

hplieninger/mpt2irt documentation built on May 17, 2019, 4:54 p.m.