MPLUS input programs for Samejima’s Graded Response Model estimation.
In this section we give the MPLUS 5.1 input programs to conduct FIML and CIFA estimation of Samejima's graded model. The data file for this example, 'ppo3.dat', comes from Maydeu-Olivares, A., Rodríguez-Fornells, A., Gómez-Benito, J. and D'Zurilla, T.J. (2000). It consists of 776 responses to the five items of the PPO scale of the Social Problem Solving Inventory-Revised (SPSI-R). The responses to the items have been tricotomized by collapsing categories 0 and 1, and 3 and 4.
The input files provided are:
1) FIML; logistic link function and unstandardized parameterization
2) CIFA-ULS; normal link function and unstandardized parameterization transformed to logistic metric
3) CIFA-ULS; normal link function and standardized parameterization transformed to logistic metric
Notice that in MPLUS, Alfa/Beta (unstandardized) parameterization is called Theta parameterization and Tau/Lambda (standardized) parameterization is called Delta parameterization.
FILE FIML.INP
TITLE: FIML;
! by default, a logistic link function is used
! by default, unstandardized parameters are used
DATA:
FILE IS ppo3.dat;
VARIABLE:
!This defines variables names
NAMES ARE y1-y5;
!This defines variables as categorical
CATEGORICAL ARE ALL;
ANALYSIS:
!This calls for Maximum Likelihood estimation
ESTIMATOR = ML;
MODEL:
!Factor loadings are free to be estimated
f1 BY y1-y5*;
!This sets latent trait variance
f1@1;
FILE CIFA_unstandardized.INP
TITLE: CIFA unstandardized parameterization;
! by default, a normal link function is used
DATA: FILE IS ppo3.dat;
VARIABLE:
!This defines variables names
NAMES ARE y1-y5;
!This defines variables
!as categorical
CATEGORICAL ARE ALL;
ANALYSIS:
!This calls for ULS
!estimator
ESTIMATOR = ULS;
TYPE = MEANSTRUCTURE;
!This line calls for
!alfa/beta unstandardized estimates
PARAMETERIZATION = THETA;
MODEL:
!Factor loadings are to be estimated
f1 BY y1-y5*;
!Latent trait variance is set to 1
f1@1;
!Latent response variance = D^2, to achieve logistic metric
! If no logistic metric is desired simply set at 1
8;
FILE CIFA_standardized.INP
TITLE: CIFA standardized
! by default, a normal link function is used
DATA: FILE IS ppo3.dat;
VARIABLE:
!This defines variables names
NAMES ARE y1-y5;
!This defines variables
!as categorical
CATEGORICAL ARE ALL;
ANALYSIS:
!This calls for ULS estimation
ESTIMATOR = ULSMV;
TYPE = MEANSTRUCTURE;
!This calls for tau/lambda standardized estimates
PARAMETERIZATION = DELTA;
MODEL:
!Factor loadings free to be estimated
f1 BY y1-y5*.5(lambda1-lambda5);
!Factor variance is set to be 1
f1@1;
!Thresholds free to be estimated
[y1$1-y5$2*](tau1-tau10);
! No further commands are needed
! The next commands are optional. Given the estimated
! standardized parameters in normal metric, they
! are transformed to unstandardized estimates in
! logistic metric
! Mplus also prints SEs for the transformed parameters
MODEL CONSTRAINT:
NEW(beta1-beta5 alfa1-alfa10);
!Lambda to beta reparameterization
beta1 = 1.702*lambda1/SQRT(1-lambda1**2);
beta2 = 1.702*lambda2/SQRT(1-lambda2**2);
beta3 = 1.702*lambda3/SQRT(1-lambda3**2);
beta4 = 1.702*lambda4/SQRT(1-lambda4**2);
beta5 = 1.702*lambda5/SQRT(1-lambda5**2);
!tau to alpha reparameterization
alfa1 =1.702*tau1/SQRT(1-lambda1**2);
alfa2 =1.702*tau2/SQRT(1-lambda1**2);
alfa3 =1.702*tau3/SQRT(1-lambda2**2);
alfa4 =1.702*tau4/SQRT(1-lambda2**2);
alfa5 =1.702*tau5/SQRT(1-lambda3**2);
alfa6 =1.702*tau6/SQRT(1-lambda3**2);
alfa7 =1.702*tau7/SQRT(1-lambda4**2);
alfa8 =1.702*tau8/SQRT(1-lambda4**2);
alfa9 =1.702*tau9/SQRT(1-lambda5**2);
alfa10 =1.702*tau10/SQRT(1-lambda5**2);