LLRA {eRm} R Documentation

## Fit Linear Logistic Models with Relaxed Assumptions (LLRA)

### Description

Automatically builds design matrix and fits LLRA.

### Usage

LLRA(X, W, mpoints, groups, baseline, itmgrps = NULL, ...)

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


### Arguments

 X Data matrix as described in Hatzinger and Rusch (2009). It must be of wide format, e.g. for each person all item answers are written in columns for t1, t2, t3 etc. Hence each row corresponds to all observations for a single person. See llraDat1 for an example. Missing values are not allowed. W Design Matrix for LLRA to be passed to LPCM. If missing, it is generated automatically. mpoints The number of time points. groups Vector, matrix or data frame with subject/treatment covariates. baseline An optional vector with the baseline values for the columns in group. itmgrps Specifies how many groups of items there are. Currently not functional but may be useful in the future. x For the print method, an object of class "llra". ... Additional arguments to be passed to and from other methods.

### Details

The function LLRA is a wrapper for LPCM to fit Linear Logistic Models with Relaxed Assumptions (LLRA). LLRA are extensions of the LPCM for the measurement of change over a number of discrete time points for a set of items. It can incorporate categorical covariate information. If no design matrix W is passed as an argument, it is built automatically from scratch.

Unless passed by the user, the baseline group is always the one with the lowest (alpha-)numerical value for argument groups. All other groups are labeled decreasingly according to the (alpha)-numerical value, e.g. with 2 treatment groups (TG1 and TG2) and one control group (CG), CG will be the baseline than TG1 and TG2. Hence the group effects are ordered like rev((unique(names(groupvec))) for naming.

Caution is advised as LLRA will fail if all changes for a group will be into a single direction (e.g. all subjects in the treatment group show improvement). Currently only data matrices are supported as arguments.

### Value

Returns an object of class 'llra' (also inheriting from class 'eRm') containing

 loglik Conditional log-likelihood. iter Number of iterations. npar Number of parameters. convergence See code output in nlm. etapar Estimated basic item parameters. These are the LLRA effect parameters. se.eta Standard errors of the estimated basic item parameters. betapar Estimated item (easiness) parameters of the virtual items (not useful for interpretation here). se.beta Standard errors of virtual item parameters (not useful for interpretation here). hessian Hessian matrix if se = TRUE. W Design matrix. X Data matrix in long format. The columns correspond to the measurement points and each persons item answers are listed susequently in rows. X01 Dichotomized data matrix. groupvec Assignment vector. call The matched call. itms The number of items.

### Warning

A warning is printed that the first two categories for polytomous items are equated to save parameters. See Hatzinger and Rusch (2009) for a justification why this is valid also from a substantive point of view.

Thomas Rusch

### References

Fischer, G.H. (1995) Linear logistic models for change. In G.H. Fischer and I. W. Molenaar (eds.), Rasch models: Foundations, recent developments and applications (pp. 157–181), New York: Springer.

Glueck, J. and Spiel, C. (1997) Item response models for repeated measures designs: Application and limitations of four different approaches. Methods of Psychological Research, 2. https://www.dgps.de/fachgruppen/methoden/mpr-online/issue2/art6/article.html

Hatzinger, R. and Rusch, T. (2009) IRT models with relaxed assumptions in eRm: A manual-like instruction. Psychology Science Quarterly, 51, pp. 87–120.

The function to build the design matrix build_W, and the S3 methods summary.llra and plotTR and plotGR for plotting.

### Examples

##Example 6 from Hatzinger & Rusch (2009)
groups <- c(rep("TG",30),rep("CG",30))
llra1

## Not run:
##An LLRA with 2 treatment groups and 1 baseline group, 5 items and 4
##time points. Item 1 is dichotomous, all others have 3, 4, 5, 6
##categories respectively.
tps <- 4

#baseline CG
ex2 <- LLRA(dats,mpoints=tps,groups=groups)

#baseline TG1
ex2a <- LLRA(dats,mpoints=tps,groups=groups,baseline="TG1")

#summarize results
summary(ex2)
summary(ex2a)

#plotting
plotGR(ex2)
plotTR(ex2)
## End(Not run)


[Package eRm version 1.0-2 Index]