EPSY 6210

04.05.2010

Logistic Regression

Forrest Lane (guest lecture); Forrest can email us the PPT

research questions (involving categorical data rather than continuous variables):

• are students with higher grades and fewer extracurricular activities more likely to pass the TAKS math test?
• does a student's gender & score on a standardized reading test predict their likelihood of being recommended for a remedial reading program?

you could use multinominal / multiple categorical variables, although Forrest hasn't tried this per se.

plotting dichotomous variables on a graph just gives you two "lines" of data -- provides a problem when trying to plot a linear relationship.

how can we transform this so that we can see the relationship?

assumptions of linear regression:

• doesn't assume a linear relationship
• dependent v. doesn't need to be normally distributed
• dependent v. doesn't need to be homoscedastic.
• doesn't require that the independents be interval.

levels of scale, criterion... (see PPT)

concept of ranking magnitude of values/importance of variables (like Beta weights or b), logit

our outcome: we'll talk about the probability of being in one group or the other

• (y' is "y prime," analogous to y-hat, a predicted score)

odds ratio: for every one unit change in x, what is the probable unit change in y (?)

how you code variables is very important, because the interpretation of numeric values (0, 1) is dependent on the categories/levels they represent.

will probably use the "probability" and "odds" equations  more than the "loglinear transformation" equation.

• in the equations, they include "a+bx" which is the regression equation. interesting!

odds ratio:

• the likelihood of that the observation or subject falls into one category versus another (given a certain characteristic or predictor variable)...?
• lower probability ("predicted probability") = less than 1
• higher probability = greater than 1 (greater than a 50-50 chance)
• 1 = both outcomes are equally likely
• in odds ratio, b is analogous to Beta, but is NOT the slope of the line
• b = 0 = no relationship between predicted variables and odds 
• (SEE OTHER SLIDES FOR THE REST)

(see "vote 2000" handout)

you run the model to use the predicted probability to obtain the most likely outcome (y prime), and compare that to the actual outcome (y) to evaluate the strength of the model.

• if the error lies mostly around .5 probability, that is to be expected. if the error is on the extremes, say near .1 or .9, that begins to be problematic for your model.

for every unit change in x (predictor variable, gender), that is your odds change in y (independent variable, candidate choice).

• outcome = "men are less likely to vote for Gore"
• male = 1, female = 0
• Gore = 1, Bush = 0
• to make a statement about women, you need to flip the categorical coding and re-run the model (the order changes what the model tests) -- that is, code females as 1 and males as 0.
• age: "as I go up a year (get older), my likelihood of voting for Gore increases" 

pi in this context simply means "probability"

• probability: probability of obtaining the specific outcome
• odds: changes as the predictor unit changes...either more or less likely. (not sure i get this. hmm.)

there are different methods for interpreting this--use judgment with the probability, the odds ratio, and the hit rate (and the omnibus test--statistical significance, etc.) to determine what your results say.

(my brain stopped working here.)