Goodness of fit

The goodness of fit or adaptation (English goodness of fit ) indicates "how well " a statistical model can explain a lot of observations. Mass of the goodness of fit permit a statement about the discrepancy between the theoretical values ​​of the tested random variables that are expected or predicted because the model and the actually measured values ​​.

The goodness of fit of a model to present data can be assessed using statistical tests or appropriate indicators.

Adaptation measures may be used in the hypothesis test to test, for example, for normality in the residuals, to check whether two samples come from populations with the same distribution or to test whether certain frequencies follow a certain distribution (see also Pearson's Chi - square test).

Example

The Chi -square statistic is the sum of the expected frequencies divided by the squared differences between the observed and expected frequencies:

Where:

The result can be compared to the chi-square distribution, to determine the goodness of fit.

Quality criteria

In structural equation models, different quality criteria have been established:

• Chi -square
• Goodness of fit index ( engl. goodness - of-fit index, GFI )
• Adjusted goodness of fit index ( engl. adjusted goodness - of-fit index, AGFI )
• Comparative adaptation index (English comparative fit index, CFI)
• Normalized adaptation index (English normed fit index, NFI)
• Approximationsdiskrepanzwurzel (English root mean square error of approximation, RMSEA )
• Standardized Residualdiskrepanzwurzel (English Standardized root mean square residual, SRMR )

As a criterion for linear regression applies the coefficient of determination.