When you put a continuous predictor into a linear regression model, you assume it has a constant relationship with the dependent variable along the predictor’s range. But how can you be certain? What is the best way to measure this?
And most important, what should you do if it clearly isn’t the case?
Let’s explore a few options for capturing a non-linear relationship between X and Y within a linear regression (yes, really). (more…)
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.
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.
Here is the result of the regression using SPSS:
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 (more…)
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. (The slopes of the lines between the response and the covariate are parallel).
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? (more…)