slopes

Segmented Regression for Non-Constant Relationships

by Jeff Meyer

We often have a continuous predictor in a model that we believe has non-constant relationship with the dependent variable along the predictor’s range. But how can we be certain? What is the best way to measure this?

Sometimes including a quadratic term will capture the change in the slope as we move from the bottom of the range to the top of the range. But a quadratic term only works in two situations:

The rate of change increases and then at some point decreases, or:
The opposite happens – the rate of change decreases and at some point increases.

We could also create a categorical variable. Each category within the categorical variable would represent a specific range within the continuous variable. [Read more…] about Segmented Regression for Non-Constant Relationships

Interpreting Interactions in Linear Regression: When SPSS and Stata Disagree, Which is Right?

by Jeff Meyer Leave a Comment

Sometimes what is most tricky about understanding your regression output is knowing exactly what your software is presenting to you.

Here’s a great example of what looks like two completely different model results from SPSS and Stata that in reality, agree.

The Model

I ran a linear model regressing “physical composite score” on education and “mental composite score”.

The outcome variable, physical composite score, is a measurement of one’s physical well-being. The predictor “education” is categorical with four categories. The other predictor, mental composite score, is continuous and measures one’s mental well-being.

I am interested in determining whether the association between physical composite score and mental composite score is different among the four levels of education. To determine this I included an interaction between mental composite score and education.

The SPSS Regression Output

Here is the result of the regression using SPSS:

Member Training: Segmented Regression

by Jeff Meyer Leave a Comment

Linear regression with a continuous predictor is set up to measure the constant relationship between that predictor and a continuous outcome.

This relationship is measured in the expected change in the outcome for each one-unit change in the predictor.

One big assumption in this kind of model, though, is that this rate of change is the same for every value of the predictor. It’s an assumption we need to question, though, because it’s not a good approach for a lot of relationships.

Segmented regression allows you to generate different slopes and/or intercepts for different segments of values of the continuous predictor. This can provide you with a wealth of information that a non-segmented regression cannot.

In this webinar, we will cover [Read more…] about Member Training: Segmented Regression

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