Lesson 19: Non-linear Models
Lesson 19: Non-linear ModelsOverview
Here we'll explore the logistic regression model and a function for least-squares fitting of arbitrarty non-linear functions.
Objectives
- 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()
R
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
19.1 - A Brief Definition of the Logistic ModelHere we'll discuss the baxic background assumptions of the Logistic regression model.
19.2 - Fitting a Logistic Model
19.2 - Fitting a Logistic ModelIn 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
19.3 - Interpreting the Coefficients of the Logistic Model INow we'll interpret the coefficients of the model we fit in the last video.
19.4 - Interpreting the Coefficients of the Logistic Model II
19.4 - Interpreting the Coefficients of the Logistic Model IIIn 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
19.5 - Logistic Regression on Individual Data IWe'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
19.6 - Logistic Regression on Individual Data IIWe'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()
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
19.8 - Interpreting an nls() ModelHere we'll examine the object created by nls().
19.9 - Using anova() on nls() Models
19.9 - Using anova() on nls() ModelsFinally we'll demonstrate the use of anova() for comparison of nested nls() models.