Variance Components and Mixed Model ANOVA/ANCOVA Method Options

Following are descriptions of the options in the Method group box on the Variance Components and Mixed Model ANOVA/ANCOVA Results dialog - Advanced tab.

Expected MS

Select the Expected MS option button to estimate the variance components of the random effects in the model by equating their variances to their expected mean squares. When this option is selected, you can then specify a Type I, Type II, or Type III decomposition of the sums of squares for the random effects by specifying the desired decomposition in the SS Type box on the Advanced tab. Also additional spreadsheets for the Summary: Components of variance button on the Advanced tab are available.

MIVQUE0

Select the MIVQUE0 option button to estimate the variance components of the random effects in the model by Minimum Variance Quadratic Unbiased Estimators (such as, MIVQUE). MIVQUE0 estimation is a variation of the Restricted Maximum Likelihood estimation technique. In MIVQUE0 estimation, there is no weighting of the random effects, so an iterative solution for estimating their variance components is not required. When the MIVQUE0 option is selected, the standard linear ANOVA techniques of decomposing sums of squares and testing the significance of effects by taking ratios of mean squares are not applicable, because a quadratic, rather than linear model is used for estimation. Therefore, when the MIVQUE0 estimation method is used, the SS and MS for Effects button on the Estimation tab is not available, and no additional spreadsheets for the Summary: Components of variance button on the Advanced tab are available.

REML and ML

Select the REML or ML option button to estimate the variance components of the random effects in the model by REML or ML estimation respectively. The basic idea behind both REML and ML estimation is to find the set of weights for the random effects in the model that minimize the negative of the natural logarithm times the likelihood of the data (the likelihood of the data can vary from zero to one, so minimizing the negative of the natural logarithm times the likelihood of the data amounts to maximizing the probability, or the likelihood, of the data). When the REML or ML estimation method is used, the SS and MS for  Effects button on the Estimation tab is not available, and additional spreadsheets for the Summary: Components of variance button on the Advanced tab are available.

Note: there are several modules in Statistica that will perform Analysis of Variance for factorial or specialized designs. For a discussion of these modules and the types of designs for which they are best suited refer to Methods for Analysis of Variance.

Note also that the General Linear Model (GLM) module can analyze designs with any number and type of between effects and compute ANOVA-based variance component estimates for any effect in a mixed-model analysis.