19 Non-linear Models
Overview
Here we’ll explore the logistic regression model and a function for least-squares fitting of arbitrary non-linear functions.
Objectives
Upon completion of this lesson, you should be able to:
- Recognize when a logistic model would be appropriate
- Fit a logistic model to proportion (group) data
- Fit a logistic model to binary (individual) data
- Interpret coefficients of the logistic model
- Fit arbitrary non-linear models using
nls()
Data and R Code Files
The R code file and data files for this lesson can be found on the Essential R - Notes on learning R page.
19.1 A Brief Definition of the Logistic Model
Here we’ll discuss the baxic background assumptions of the logistic regression model.
19.2 Fitting a Logistic Model
In this video, we’ll examine a data set which shows group proportions (so any value between 0 and 1 is possible) and fit a logistic regression to the data.
19.3 Interpreting the Coefficients of the Logistic Model I
Now we’ll interpret the coefficients of the model we fit in the last video.
19.4 Interpreting the Coefficients of the Logistic Model II
In this video, we’ll plot our regression model over the data and add our midpoint as calculated from the coefficients.
19.5 Logistic Regression on Individual Data I
We’ll try a different data set now, where each case is binary (either “a” or “b”), but we’ll see we can still fit a logistic regression.
19.6 Logistic Regression on Individual Data II
We’ll wind up our discussion of logistic regression by examining the model we fit in the last video.
19.7 Other Non-linear Models Using nls()
Now we can move on to introduce nls() for fitting “non-linear least squares” models. We’ll demonstrate with some data for enzyme kinetics that exhibit Michaelis-Menten dynamics.
19.8 Interpreting an nls() Model
Here we’ll examine the object created by nls().
19.9 Using anova() on nls() Models
Finally we’ll demonstrate the use of anova() for comparison of nested nls() models.