The Analysis Factor
Statistical Consulting, Resources, and Statistics Workshops for Researchers
A well-fitting regression model results in predicted values close to the observed data values. 
The mean model, which uses the mean for every predicted value, generally would be used if there were no useful predictor variables. The fit of a proposed regression model should therefore be better than the fit of the mean model. [Read more…] about Measures of Model Fit for Linear Regression Models
The great majority of all regression modeling explores and tests the association between independent and dependent variables. We are not able to claim the independent variable(s) has a causal relationship with the dependent variable. There are five specific model types that allow us to test for causality. Difference in differences models are one of the five.
[Read more…] about Member Training: Difference in Differences
Multicollinearity can affect any regression model with more than one predictor. It occurs when two or more predictor variables overlap so much in what they measure that their effects are indistinguishable.
When the model tries to estimate their unique effects, it goes wonky (yes, that’s a technical term).
So for example, you may be interested in understanding the separate effects of altitude and temperature on the growth of a certain species of mountain tree.
It was Casey Stengel who offered the sage advice, “If you come to a fork in the road, take it.”
When you need to fit a regression model to survival data, you have to take a fork in the road. One road asks you to make a distributional assumption about your data and the other does not. [Read more…] about Parametric or Semi-Parametric Models in Survival Analysis?
When I was in graduate school, stat professors would say “ANOVA is just a special case of linear regression.” But they never explained why.
And I couldn’t figure it out.
The model notation is different.
The output looks different.
The vocabulary is different.
The focus of what we’re testing is completely different. How can they be the same model?
[Read more…] about Why ANOVA is Really a Linear Regression, Despite the Difference in Notation
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.
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.
Answer:
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. [Read more…] about Can We Use PCA for Reducing Both Predictors and Response Variables?