Estimation of Variance Components - Technical Overview

Select the Advanced tab of the Variance Components and Mixed Model ANOVA/ANCOVA Results dialog to access the options described here.

Dependent variables. Click the Dependent variables button to display the standard variable selection dialog, from which you can select the dependent variables to analyze by highlighting those variables on the list. If multiple dependent variables are specified for the analysis, use this option to select a single dependent variable or a subset of dependent variables to analyze.

Note: missing data. If multiple dependent variables are selected for the analysis, STATISTICA will apply casewise deletion of missing data; that is, cases or runs will be deleted from the analysis if there are missing data for any of the dependent variables specified for the analysis. For consistency in the results, casewise deletion of missing data is applied even if only a single dependent variable is selected to be analyzed from a larger list of multiple dependent variables selected for the analysis on the Variance Components and Mixed Model ANOVA/ANCOVA Startup Panel - Quick tab. Thus, be careful when there are missing data present in your dependent variables; the results for those variables without missing data may not be based on all available information (namely, those runs where some other dependent variable had missing data were dropped from the analysis).

Summary:
Components of variance. Click the Summary:
Components of variance button to create a spreadsheet that displays
the variance
components for each random
effect in the model for each dependent variable.

Additional spreadsheets. A list of additional spreadsheets that can be displayed when you click the Summary: Components of variance button are listed below the button. Select the check box adjacent to the additional spreadsheet(s) that you want to display, and then click the Summary button to view these spreadsheets. The list of additional spreadsheets will change depending on the Method that has been selected for estimating variance components (see below). For more information on the additional spreadsheets that can be displayed, see Summary: Components of Variance Spreadsheets.

Stacked bar plot. Click the Stacked bar plot button to display a stacked bar plot of the estimated variance components, showing the magnitude of each variance component. If more than one dependent variable has been selected to be analyzed, a compound graph including a stacked bar plot of the variance components for each dependent variable will be produced. If the Plot relative variances check box is selected, relative percentages of the nonzero variance components will be plotted.

Pie chart. Click the Pie chart button to display a pie chart of the estimated variance components, showing the magnitude of each variance component. If more than one dependent variable has been selected to be analyzed, multiple pie charts, one for each dependent variable, will be produced. If the Plot relative variances check box is selected, relative percentages of the nonzero variance components will be charted.

Plot relative variances (% of total). Select the Plot relative variances check box to plot the estimated variance components in terms of percentages of total variance when Stacked bar plots or Pie charts are requested. Note that estimated population intraclass correlation coefficients are displayed on Stacked bar plots and Pie charts when the Plot relative variances check box is selected. These relative variances can be interpreted as zero-order intraclass correlations when there is only one random factor in the analysis. If there is more than one random effect in the analysis and the random effects are correlated, the relative variances should be interpreted as partial intraclass correlations.

Method. Under Method, choose the method to be used for estimating the variance components for the random effects. See Method Options for further details about these options.

SS Type. The options under SS type are used to choose the type of sums of squares decomposition when estimating the variance components for the random effects in the model using Expected MS (mean squares) as the Method (see above).

Type I. Select the
Type I option button to attribute shared variation between effects
to the effect which enters the model first, as determined by the order
in which they were selected to be included in the model. Unlike the Type II or Type
III decompositions, this
decomposition produces sums of squares for the effects that add up to
the total sums of squares. Type I sums of squares, however, typically
depend on the order in which effects are included in the model.

Type II. Select the
Type II option button to test an effect in the presence of all
other effects except any higher order interactions in which it is involved.
Type II sums of squares typically do not add up to the total sums of squares.

Type III. Select the
Type III option button to specify that shared variance between
effects is not attributed to any effect. Type III sums of squares do not
depend on the order in which effects are entered in the model, but typically
do not add up to the total sums of squares.

Note that 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 using any of the six types of sums of squares.