Scientific Software International (SSI) publishes statistical data analysis software: LISREL (structural equation model/SEM, survey generalized linear model/SGLIM), 
HLM (hierarchical linear modeling, multilevel model), SuperMix (mixed models, mixed-effects program, MIXREG, MIXOR, MIXNO and MIXPREG) and Item Response Theory/IRT (BILOG-MG, MULTILOG, PARSCALE)Scientific Software International (SSI) publishes statistical data analysis software: LISREL (structural equation model/SEM, survey generalized linear model/SGLIM), 
HLM (hierarchical linear modeling, multilevel model), SuperMix (mixed models, mixed-effects program, MIXREG, MIXOR, MIXNO and MIXPREG) and Item Response Theory/IRT (BILOG-MG, MULTILOG, PARSCALE)Scientific Software International (SSI) publishes statistical data analysis software: LISREL (structural equation model/SEM, survey generalized linear model/SGLIM), 
HLM (hierarchical linear modeling, multilevel model), SuperMix (mixed models, mixed-effects program, MIXREG, MIXOR, MIXNO and MIXPREG) and Item Response Theory/IRT (BILOG-MG, MULTILOG, PARSCALE)


D  Data

The data were provided by Scott Chaiken of Armstrong Laboratory, Brooks Air Force Base and and are described in Blozis (2004). It presents performance on two procedural tasks developed for the assessment of quantitative and verbal skill acquisition. Both response times and accuracy scores were recorded for a total of 384 trails for each task. Data for 228 corded are considered. Response times for each test were aggregated separately into 12 blocks of 32 trail each. A selection of this data set is provided in the file QUANT.PSF in the SLCEX subfolder. The first portion of QUANT.PSF is shown in the following PSF window.

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M  Model

The model to be fitted to the data in QUANT.PSF is an exponential latent curve. This is accomplished by using the methods in Browne (1993). A path diagram of the corresponding model is shown below.

Remarks

  • The variables QT4, QT5, ..., and QT12 denote the aggregate quantitative scores for blocks 4, 5, ... , and 12.
  • The latent variables Initial, Potent and Rate denote the initial performance, the potential performance and the rate of learning respectively.

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A  Analysis
  • Select the New option from the File menu to load the New dialog box.
  • Select the Syntax Only option on the New list box as shown below

    to open the blank SYNTAX1 text editor window.
  • Select the Save option from the File menu to load the Save As dialog box .
  • Type the file name SLCEX7A.LS8 in the File name string field to produce the following dialog box.

  • Click on the Save button to open the text editor window for SLCEX7A.LS8.
  • Enter the following commands in the text editor window for SLCEX7A.LS8.
    • Line 1 is a comment statement.
    • Line 2 specifies that the data in QUANT.PSF contains 228 observations of 12 variables.
    • Line 3 specifies the raw data file to be used.
    • Lines 4 and 5 specify that only the final 9 variables will be used in the analysis.

  • Enter the following commands in the text editor window for SLCEX7A.LS8.

    • Line 1 is a comment statement
    • Line 2 specifies that the LISREL model has 9 indicators of 3 latent variables, all the factor loadings are unknown parameters, the 3 latent variables are correlated, the measurement errors are uncorrelated, the latent variable means are unknown parameters and the model includes 3 additional parameters.
    • Lines 3 and 4 specify labels for the 3 latent variables.
    • Lines 5 to 8 specify the structure for the latent variable means.

  • Enter the following commands in the text editor window for SLCEX7A.LS8.

    • Line 1 is a comment statement.
    • Lines 2 to 10 specify the structure of the coefficients of the potential performance basis curve.
    • Line 11 is a comment statement.
    • Lines 12 to 20 specify the structure of the coefficients of the initial performance basis curve.
    • Line 21 is a comment statement.
    • Lines 22 to 30 specify the structure of the coefficients of the learning basis curve.
    • Line 31 is a comment statement.
    • Line 32 specifies equal error variances for the 9 scores.

  • Go ahead by entering the following commands in the text editor window for SLCEX7A.LS8.

    • Line 1 is a comment statement.
    • Lines 2 to 4 specify starting values for the potential performance, the initial performance and the performance rate.
    • Lines 5 to 8 specify the starting values for the variances and covariances of the 3 latent variables.
    • Line 9 specifies a starting value for the common error variance.
    • Line 10 requests a path diagram for the LISREL model.
    • Line 11 specifies that 3 decimal places should be used for the results written to the LISREL output file, the user-specified starting values should be used and requests the completely standardized estimates of the unknown parameters of the LISREL model.

  • Click on the Run LISREL toolbar icon to produce the following PTH window for SLCEX7A.PTH.

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