# MANOVA

### Can We Use PCA for Reducing Both Predictors and Response Variables?

January 20th, 2017 by

I recently gave a free webinar on Principal Component Analysis. We had almost 300 researchers attend and didn’t get through all the questions. This is part of a series of answers to those questions.

If you missed it, you can get the webinar recording here.

### Question: Can we use PCA for reducing both predictors and response variables?

In fact, there were a few related but separate questions about using and interpreting the resulting component scores, so I’ll answer them together here.

### Let’s say I would like to interpret my regression results in terms of original data, but they are hiding under PCAs. What is the best interpretation that we can do in this case?

So yes, the point of PCA is to reduce variables — create an index score variable that is an optimally weighted combination of a group of correlated variables.

And yes, you can use this index variable as either a predictor or response variable.

It is often used as a solution for multicollinearity among predictor variables in a regression model. Rather than include multiple correlated predictors, none of which is significant, if you can combine them using PCA, then use that.

It’s also used as a solution to avoid inflated familywise Type I error caused by running the same analysis on multiple correlated outcome variables. Combine the correlated outcomes using PCA, then use that as the single outcome variable. (This is, incidentally, what MANOVA does).

In both cases, you can no longer interpret the individual variables.

You may want to, but you can’t. (more…)

### Member Training: MANOVA

June 1st, 2013 by

MANOVA is the multivariate (meaning multiple dependent variables) version of ANOVA, but there are many misconceptions about it.

In this webinar, you’ll learn:

• When to use MANOVA and when you’d be better off using individual ANOVAs
• How to follow up the overall MANOVA results to interpret
• What those strange statistics mean — Wilk’s lambda, Roy’s Greatest Root (hint — it’s not a carrot)
• Its relationship to discriminant analysis

Note: This training is an exclusive benefit to members of the Statistically Speaking Membership Program and part of the Stat’s Amore Trainings Series. Each Stat’s Amore Training is approximately 90 minutes long.

Not a Member? Join!