Estimation of the parameters of a Rasch model, tests and specific graphs
raschtestv7 varlist [if exp] [in range] , id(varname) [method(keyword) nold iterate(#) test(keyword) difficulties(vector) meandiff details group(numlist) autogroup covariates(varlist[, ss1 ss3]) dirsave(directory) filessave pause replace nodraw icc information splittest fitgraph genlt(newvarname[,replace]) genscore(newvarname) genfit(newvarlist) comp(varname) dif(varlist) trace time]
raschtest varlist [if exp] [in range] [, options_of_raschtestv7 graph]
varlist is a list of two existing binary variables or more.
Description
raschtest estimates the parameters of a Rasch model. The estimation method can be chosen between conditional maximum likelihood (CML), marginal maximum likelihood (MML) and generalized estimating equations (GEE). raschtest offer a set of tests, to valuate the fit of the data to the Rasch model, or detect non homogeneous items (Andersen Z test, First order test (Q1, R1c, R1m, or Wright Panchapakesan), U test, Split test) and indexes (OUTFIT and INFIT per items or per individuals). Several graphical representations can be easily obtained: comparison of the observed and theorical Item Characteristic Curves (ICC), Map difficulty parameters/Scores, results of the split tests, and information function.
Options
method specifies the used method to estimate the difficulty parameter among CML (method(cml) - by default), MML (method(mml)) or GEE (method(gee)).
nold avoids the Listwise Deletion of the individuals with missing data. By default, all the individuals with one or more missing data are omited.
iterate allows defining the maximal number of iterations of the maximisation algorithm. By default, this number is fixed to 200.
test specifies the tests to use among test(R) (by default, for the R1c or the R1m test), test(WP) (for the Wright- Panchapakesan test) and test(Q) (for the Q1 test).
difficulties allows fixing the values of the difficulties parameters of the items. The vector must be a row vector and must contain as many values as items. This option is available only with method(mml).
meandiff centers the difficulty parameters (only with method(cml)): by default for the CML estimations, the difficulty parameter to the last item is fixed to 0. With meandiff, only the diagonal elements of the covariance matrix of these parameters are estimated.
details displays for each group of scores a table containing the observed and expected number of positive responses and the contribution of this group to the global first-order statistic.
group specifies groups of scores, by defining the superior limits of each group (note that the score "0" and this one corresponding to the number of items are always isolated).
autogroup automatically creates groups of scores (with at least 30 individuals per group).
covariates allows introducing covariates on the model. The ss1 and ss3 options allows to computes the type 1 and type 3 sums of squares to explain the variance of the latent trait by these covariates. This option is available only with method(mml).
dirsave specifies the directory where the graphs will be saved (by default, the directory defined in c(pwd)).
filessave saves all the graphs in .gph files (by default, the graphs are not saved).
pause allows to made a pause between the displaying of each graph.
replace specifies that the existing graphical files will be replaced.
nodraw avoids displaying of the graphs.
icc displays, for each item, the observed and expected (under the Rasch model) ICC in a graph.
graph represents in the same graph the distributions of the difficulty parameters, this one of the scores, and [with method(mml) or method(gee)] the expected distribution of the latent trait, in function of the latent trait.
information represents the information function for the set of the items in function of the latent trait.
splittest represents, for each item, the CML estimations of the difficulty parameters for the others items in the two sub-samples defined by the individuals who have positively respond to the splitting item for the first group, and by the individuals who have negatively respond to the splitting item for the second one.
fitgraph represents four graphs. The first one concerns the OUTFIT indexes for each item, the second one, the INFIT indexes for each item, the third one the OUTFIT indexes for each individual, and the last one the INFIT indexes for each individual.
genlt creates a new variable containing, for each individual, the estimated value of the latent trait. The replace option allows replacing an existing variable.
genscore creates a new variable containing, for each individual, the value of the score.
genfit creates several new variables. newvarlist contains two words. The first one represents "outfit" and the second one "infit". This option generates two variables with this names for the OUTFIT and INFIT indexes for each individual, and the variables "outfitXX" (by replacing "outfit" by the first word) for the contribution of the item XX to the OUTFIT index (Note that the new variables contain unstandardized OUTFIT and INFIT indices, even the program displays standardized statistics in the results table and with the fitgraph option).
comp tests the equality of the means of the latent trait for two groups of individuals defined by a binary variable (only with method(mml) or method(gee)).
dif tests the Differential Item Functioning (DIF) on a list of variables by likelihood ration tests. For each variable defined in the list, the items parameters are estimated in each groups defined by this variable, and the test considers the null assumption: the estimations are the same in each group. The statistic of the test follows a chi-square distribution under the null assumption. The variable defined in the dif option must have 10 or less modalities, coded from 0 or 1 to an integer k<=10. This option is available only with method(cml).
trace displays more outputs during the running of the module.
time displays the number of seconds to run the module.
Outputs
e(N): Number of observations
e(ll): (Marginal) Log-likelihood
e(cll): Conditional log-likelihood
e(AIC): Akaike Information Criterion
e(PSI) and e(PSIadj): Personal Separation Indexes (only for meth(mml)
e(sigma): Estimated standard deviation of the latent trait
e(sesigma): Standard error of the estimated standard deviation of the latent trait
e(beta): Estimated difficulty parameters
e(Varbeta): Covariance matrix of the estimated difficulty parameters
e(theta): Estimated values for the latent trait for each value of the score
e(Varbeta): Covariance matrix for the estimated values for the latent trait for each value of the score
e(itemFit): Statistics of fit for each item (first order statistic, degree of freedom, p-value, OUTFIT index, INFIT index, and (if method(cml)) U-test statistic
e(globalFit): Global first order test (statistic, degrees of freedom, p-value)
e(AndersenZ): Andersen LR Z test (first order statistic, degree of freedom, p-value) (if method(cml))
e(DIF): DIF LR Z test (statistic, degree of freedom, p-value for each variable defined in dif) (if method(cml))
e(Zcomp) and e(pZcomp): Statistics of test and associated p-value for the test of comparison of the two population defined with the comp option.
e(betacovariates), e(Vbetacovariates), e(zcovariates) and e(pcovariates): respectivelly the estimated values of the parameters associated to the covariates, the covariance matrix of the estimations, the statistics of the tests to compare the parameters to 0 and the associated p-values (only with the covariates option)
Examples
. raschtest item1-item9, id(id) /*estimates the parameters by CML approach*/
. raschtest item*, id(id) method(gee) information icc dirsave(c:\graphs) filesnames(graphs) /*estimates the parameters by GEE, draw the information graph and the ICCs and save the graphical representations under gph files*/
. raschtest item1 item4 item7 item 18 item23 item35-item39 , id(id) group(2 3 4 5) test(WP) split graph /*creates groups of score (1 and 2, 3, 4, 5 and more) to compute the Wright Panchapakesan tests, computes the split test, and represent the map difficulty parameters/scores*/
. matrix diff=(-1,-.5,0,.5,1) . raschtest item1-item5 , id(id) diff(diff) covariable(group sex age,ss1 ss3) nold /*difficulties parameters are fixed, 3 covariables are introduced, no listwise deletion*/
Author
Jean-Benoit Hardouin, PhD, assistant professor EA 4275 "Team of Biostatistics, Clinical Research and Subjective Measures in Health Sciences" University of Nantes - Faculty of Pharmaceutical Sciences 1, rue Gaston Veil - BP 53508 44035 Nantes Cedex 1 - FRANCE Email: jean-benoit.hardouin@univ-nantes.fr Websites AnaQol and FreeIRT
Also see
Online: help for xtlogit, clogit and geekel2d and gllamm if installed.