ThurMod (version 1.1.11)

fit.correct: Correct degree of freedom and fit indices in Thurstonian block models

Description

Correct fit indices (RMSEA and CFI) by correcting the degrees of freedom after estimation a Thurstonian model.

Usage

fit.correct(n, blocks, chi2_mod, df_mod, chi2_base, df_base)

Value

Returns a vector containing corrected degrees of freedom, and the corrected RMSEA and CFI values.

Arguments

n

The number of respondents.

blocks

A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block.

chi2_mod

The \(\chi^2\) value of the estimated model.

df_mod

The degrees of freedom of the estimated model.

chi2_base

The \(\chi^2\) value of the baseline model.

df_base

The degrees of freedom of the baseline model.

Details

If a ranking design is used (variances of binary indicators is zero) there are redundancies among the thresholds and tetrachoric correlations to be estimated. This is the case, whenever the number of items per block is larger than two. In these cases the degrees of freedom must be corrected by subtracting the redundancies. For more details see Jansen and Schulze (2023) and Maydeu-Olivares (1999).

References

Jansen, M. T., & Schulze, R. (in review). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data.

Maydeu-Olivares, A. (1999). Thurstonian modeling of ranking data via mean and covariance structure analysis. Psychometrika, 64(3), 325-340. tools:::Rd_expr_doi("10.1007/BF02294299")

Examples

# Define 30 items divided by ten triplets as blocks
blocks <- matrix(c(1:30), ncol = 3)

# Assume the model yield the following fit, with 426 respondents
# chi2_mod = 224.456, df_mod = 59, chi2_base = 1056.566, df_base = 90

fit.correct(426,blocks,224.456,59,1056.566,90)

# The corrected values are rmsea = 0.0917892; cfi =  0.8184749