Assumptions

The Difference Between Model Assumptions, Inference Assumptions, and Data Issues

Have you ever compared the list of assumptions for linear regression across two sources? Whether they’re textbooks, lecture notes, or web pages, chances are the assumptions don’t quite line up.

Why? Sometimes the authors use different terminology. So it just looks different.

And sometimes they’re including not only model assumptions, but inference assumptions and data issues. All are important, but understanding the role of each can help you understand what applies in your situation.

Member Training: Using Transformations to Improve Your Linear Regression Model

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Transformations don’t always help, but when they do, they can improve your linear regression model in several ways simultaneously.

They can help you better meet the linear regression assumptions of normality and homoscedascity (i.e., equal variances). They also can help avoid some of the artifacts caused by boundary limits in your dependent variable — and sometimes even remove a difficult-to-interpret interaction.

ANCOVA Assumptions: When Slopes are Unequal

by Karen Grace-Martin 18 Comments

There are two oft-cited assumptions for Analysis of Covariance (ANCOVA), which is used to assess the effect of a categorical independent variable on a numerical dependent variable while controlling for a numerical covariate:

1. The independent variable and the covariate are independent of each other.

2. There is no interaction between independent variable and the covariate.

In a previous post, I showed a detailed example for an observational study where the first assumption is irrelevant, but I have gotten a number of questions about the second.

So what does it mean, and what should you do, if you find an interaction between the categorical IV and the continuous covariate? [Read more…] about ANCOVA Assumptions: When Slopes are Unequal

When Assumptions of ANCOVA are Irrelevant

by Karen Grace-Martin 42 Comments

Every once in a while, I work with a client who is stuck between a particular statistical rock and hard place.

It happens when they’re trying to run an analysis of covariance (ANCOVA) model because they have a categorical independent variable and a continuous covariate.

The problem arises when a coauthor, committee member, or reviewer insists that ANCOVA is inappropriate in this situation because one of the following ANCOVA assumptions are not met:

1. The independent variable and the covariate are independent of each other.

2. There is no interaction between independent variable and the covariate.

If you look them up in any design of experiments textbook, which is usually where you’ll find information about ANOVA and ANCOVA, you will indeed find these assumptions. So the critic has nice references.

However, this is a case where it’s important to stop and think about whether the assumptions apply to your situation, and how dealing with the assumption will affect the analysis and the conclusions you can draw. [Read more...] about When Assumptions of ANCOVA are Irrelevant

Assumptions of Linear Models are about Residuals, not the Response Variable

by Karen Grace-Martin 6 Comments

I recently received a great question in a comment about whether the assumptions of normality, constant variance, and independence in linear models are about the residuals or the response variable.

The asker had a situation where Y, the response, was not normally distributed, but the residuals were.

Quick Answer: It’s just the residuals.

In fact, if you look at any (good) statistics textbook on linear models, you’ll see below the model, stating the assumptions: [Read more…] about Assumptions of Linear Models are about Residuals, not the Response Variable

6 Types of Dependent Variables that will Never Meet the Linear Model Normality Assumption

by Karen Grace-Martin 11 Comments

The assumptions of normality and constant variance in a linear model (both OLS regression and ANOVA) are quite robust to departures. That means that even if the assumptions aren’t met perfectly, the resulting p-values will still be reasonable estimates.

But you need to check the assumptions anyway, because some departures are so far that the p-value become inaccurate. And in many cases there are remedial measures you can take to turn non-normal residuals into normal ones.

But sometimes you can’t.

Sometimes it’s because the dependent variable just isn’t appropriate for a linear model. The [Read more…] about 6 Types of Dependent Variables that will Never Meet the Linear Model Normality Assumption