This chapter describes various adjustments that are needed for the traditional chi-square test statistics for goodness of fit, test of independency, and homogeneity for categorical data and analysis when data are obtained from complex survey designs.
Hosmer Lemeshow χ statistics for goodness of fit indicated that predictors sufficiently described the data.
Finally, Hosmer Lemeshow χ statistics for goodness of fit were performed.
The statistics of the goodness-of-fit test showed a satisfactory calibration (C = 3.47; p = 0.901).
At the bottom of the table, we report some test statistics and measures of goodness of fit.
A variety of indices comprising absolute fit indices (χ2 statistics; goodness-of-fit index, GFI; standardised root mean residual, SRMR), parsimonious indices (root mean square error of approximation, RMSEA) and incremental fit indices (comparative fit index, CFI; Tucker-Lewis index, TLI) were employed in this study.
The overall fit of the model to the data was evaluated through Chi square statistics, goodness-of-fit index (GFI), comparative fit index (CFI), normed fit index (NFI), incremental fit index (IFI), standardized root mean square residual (SRMR), and root mean square error of approximation (RMSEA).
The three covariance models were compared in both the DSPR and CEGS populations using four penalized fit statistics: adjusted goodness-of-fit (AGFI), parsimonious goodness-of-fit (PGFI), consistent Akaike's information criterion (CAIC), and Bayesian information criterion (BIC) (Additional file 1: Table S1).
These statistics reward goodness of fit but depreciate the number of free parameters of the model (the lowest value denotes the model that best explains the data with a minimum of free parameters).
Adequacy of the model fit was assessed using chi-square statistics, the Goodness of Fit index (GFI), the Incremental Fit Index (IFI), the Normed Fit Index (NFI) and the Comparative Fit Index [ 31].
