Transcript Probit Regression

Multinomial Logistic Regression

Read the data


use http://www.ats.ucla.edu/stat/stata/dae/mlogit,
clear
Describe the data




Codebook
Summarize
Tabulate
Make graphs
The outcome variable is brand. The variable female is
coded as 0 for male and 1 for female. Let's start with
some descriptive statistics of the variables of our
interest.
Using the Multinomial Logit Model
Now we have warmed up to building our model. Our
goal is to associate the brand choices with age and
gender. We will assume a linear relationship between
the transformed outcome variable and our predictor
variables female and age. Since there are multiple
categories, we will choose a base category as the
comparison group. Here our choice is the first brand
(brand=1).

The output above has two parts, labeled with the
categories of the outcome variable brand.
log(P(brand=2)/P(brand=1)) = b_10 + b_11*female +
b_12*age
log(P(brand=3)/P(brand=1)) = b_20 + b_21*female +
b_22*age,
with b's being the raw regression coefficients from the
output.
For example, we can say that for one unit change in the
variable age, the log of the ratio of the two
probabilities, P(brand=2)/P(brand=1), will be increased
by 0.368, and the log of the ratio of the two
probabilities P(brand=3)/P(brand=1) will be increased
by 0.686.
 Therefore, we can say that, in general, the older a
person is, the more he/she will prefer brand 2 or 3.

The ratio of the probability of choosing one outcome
category over the probability of choosing the reference
category is often referred as relative risk (and it is also
sometimes referred as odds).
 We can use the rrr option for mlogit command to
display the regression results in the language of risk.

We can also present the regression result graphically.
For example, we can create three variables p1, p2 and
p3 for the predicted probabilities and plot them against
a predictor variable. In the example below, we plot p1
against age separated by the variable female.
1
.8
.6
.4
.2
0
25
30
35
age
male
female
40