One question that seems to come up pretty often is:
What is the difference between logistic and probit regression?
Well, let’s start with how they’re the same:
Both are types of generalized linear models. This means they have this form:
Regression models
The Difference Between Logistic and Probit Regression
May 12th, 2017 by Karen Grace-Martin
Member Training: Segmented Regression
April 3rd, 2017 by Jeff Meyer
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…)
Can We Use PCA for Reducing Both Predictors and Response Variables?
January 20th, 2017 by Karen Grace-Martin
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.
How could you use the component scores?
A lot of times PCAs are used for further analysis — say, regression. How can we interpret the results of regression?
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?
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. (more…)
Analyzing Zero-Truncated Count Data: Length of Stay in the ICU for Flu Victims
January 9th, 2017 by Jeff Meyer
It’s that time of year: flu season.
Let’s imagine you have been asked to determine the factors that will help a hospital determine the length of stay in the intensive care unit (ICU) once a patient is admitted.
The hospital tells you that once the patient is admitted to the ICU, he or she has a day count of one. As soon as they spend 24 hours plus 1 minute, they have stayed an additional day.
Clearly this is count data. There are no fractions, only whole numbers.
To help us explore this analysis, let’s look at real data from the State of Illinois. We know the patients’ ages, gender, race and type of hospital (state vs. private).
A partial frequency distribution looks like this: (more…)
Two-Way Tables and Count Models: Expected and Predicted Counts
December 29th, 2016 by Jeff Meyer
In a previous article, we discussed how incidence rate ratios calculated in a Poisson regression can be determined from a two-way table of categorical variables.
Statistical software can also calculate the expected (aka predicted) count for each group. Below is the actual and expected count of the number of boys and girls participating and not participating in organized sports.
The value in the top of each cell is the actual count (40 boys do not play organized sports) and the bottom value is the expected/predicted count (36 boys are predicted to not play organized sports).
The Poisson model that we ran in the previous article generated the following table: (more…)
Understanding Incidence Rate Ratios through the Eyes of a Two-Way Table
December 27th, 2016 by Jeff Meyer
The coefficients of count model regression tables are shown in either logged form or as incidence rate ratios. Trying to explain the coefficients in logged form can be a difficult process.
Incidence rate ratios are much easier to explain. You probably didn’t realize you’ve seen incidence rate ratios before, expressed differently.
Let’s look at an example.
A school district was interested in how many children in their sixth grade classes played on organized sports teams. So they did a count and also noted the gender of the child. The results were put into a table: (more…)