Зависимость факторов в ANOVA Опции

[Pinus]

Возник такой вопрос (вдруг откуда не возьмись). Можно ли включать в план ANOVA взаимозависимые факторы? В регрессионном анализе нельзя, и об этом везде предупреждается. А вот в отношении дисперсионного анализа не встречал таких ограничений. Склоняюсь к тому, что можно, и эта взаимозависимость учитывается эффектом от взаимодействия (X*Z). Правильно ли рассуждаю?

[nokh]

Из http://faculty.chass.ncsu.edu/garson/PA765/anova.htm

Data independence. In most ANOVA designs, it is assumed the independents are orthogonal (uncorrelated, independent). This corresponds to the absence of multicollinearity in regression models. If there is such lack of independence, then the ratio of the between to within variances will not follow the F distribution assumed for significance testing. If all cells in a factorial design have approximately equal numbers of cases, orthogonality is assured because there will be no association in the design matrix table. In factorial designs, orthogonality is assured by equalizing the number of cases in each cell of the design matrix table, either through original sampling or by post-hoc sampling of cells with larger frequencies. Note, however, that there are other designs for correlated independents, including repeated measures designs, using different computation.

What designs are available in ANOVA for correlated independents?

Correlation of independents is common in non-experimental applications of ANOVA. Such correlation violates one of the assumptions of usual ANOVA designs. When correlation exists, the sum of squares reflecting the main effect of an independent no longer represents the unique effect of that variable. The general procedure for dealing with correlated independents in ANOVA involves taking one independent at a time, computing its sum of squares, then allocating the remaining sum to the other independents. One will get different solutions depending on the order in which the independents are considered. Order of entry is set by common logic (ex., race or gender cannot be determined by such variables as opinion or income, and thus should be entered first). If there is no evident logic to the variables, a rule of thumb is to consider them in the order of magnitude of their sums of squares. See Iverson and Norpoth (1987: 58-64).