Log-Linear Analysis of Frequency Tables

Select the Advanced tab of the Log-Linear Analysis Results dialog box to access the options described here.

Summary: Goodness of fit. Click the Summary: Goodness of fit button to create a spreadsheet containing the Maximum Likelihood Chi-square value and the Pearson Chi-square value, along with their corresponding degrees of freedom and p-values. You can evaluate the statistical significance of the goodness-of-fit of a particular model via the Chi-square tests.

Observed table. Click the Observed table button to display the Specify how to Review the Table dialog box, in which you specify how to review the multi-way frequency table in the most flexible manner, slice by slice as you specify. If there are more than two factors in the frequency table, you can view any two-way table within each of the levels of the remaining factors.

Fitted table. Click the Fitted table button to review the fitted table in the same manner (slice by slice) as described in Observed table (see above).

Marginal tables. Click the Marginal tables button to review the marginal tables, as specified by the current model, that were fit to the observed table. These tables will be displayed one by one, and slice by slice if marginal tables involving more than two factors are displayed.

Note that the marginal tables will include the Delta constant, as specified on the Model Specification dialog box. Therefore, when using Log-Linear as a crosstabulation program make sure that Delta is set to 0; otherwise you will not obtain accurate marginal counts.

Residuals (observed-fitted). Click the Residuals (observed-fitted) button to review the residualized table (i.e., the table of observed minus fitted frequencies), in the same manner (slice by slice) as described above.

Residuals standardized. Click the Residuals standardized button to review the table of standardized residuals, in the same manner (slice by slice) as described in Observed table (above). Standardized residuals (sijk..) are computed as:

sijk..= (fijk.. -Fijk..)/(Fijk..)½

Fijk.. denotes the fitted or expected cell frequency for cell i,j,k,...; fijk.. denotes the observed frequency.

Plot of observed vs. fitted. Click the Plot of observed vs. fitted button to display a scatterplot of the observed versus fitted (expected) frequencies. This graph is very useful for evaluating the overall fit of the model for different magnitudes of frequencies, and for detecting outliers.

Plot of fitted vs. residuals. Click the Plot of fitted vs. residuals button to display a scatterplot of the fitted frequencies versus residual frequencies (observed minus fitted). This graph is very useful for evaluating the overall fit of the model for different magnitudes of frequencies, and for detecting outliers.