How to intepret a factor response model?
On Wed, 4 May 2005, Maciej [iso-8859-2] BliziDski wrote:
I'd like to create a model with a factor-type response variable. This is an example:
What you have done here is to fit a logistic regression. The interpretation of that is covered in many good books: for example there are plots of the predicted values in MASS4. I do wonder if that is what you intended, though. You have fitted a model of 'two or three' vs 'one'. You may have intended a multinomial logistic model: again MASS4 has details of such models.
mydata <- data.frame(factor_var = as.factor(c(rep('one', 100), rep('two', 100), rep('three', 100))), real_var = c(rnorm(150), rnorm(150) + 5))
summary(mydata)
factor_var real_var
one :100 Min. :-2.742877
three:100 1st Qu.:-0.009493
two :100 Median : 2.361669
Mean : 2.490411
3rd Qu.: 4.822394
Max. : 6.924588
mymodel = glm(factor_var ~ real_var, family = 'binomial', data = mydata) summary(mymodel)
Call:
glm(formula = factor_var ~ real_var, family = "binomial", data = mydata)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.7442 -0.6774 0.1849 0.3133 2.1187
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.6798 0.1882 -3.613 0.000303 ***
real_var 0.8971 0.1066 8.417 < 2e-16 ***
---
Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 381.91 on 299 degrees of freedom
Residual deviance: 213.31 on 298 degrees of freedom
AIC: 217.31
Number of Fisher Scoring iterations: 6
---------------------------------------------------------------------
For models with real-type response variable it's easy to figure out,
what's the equation for the response variable (in the model). But here
- how do I interpret the model?
Brian D. Ripley, ripley at stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595