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Logistic Regression

- With linear regression we predicted an outcome or

dependent variable Y (measured at the interval or

ratio level) using one or more predictor

variables (Xs) also measured at the interval or

ratio level. - With logistic regression, we can predict an

outcome or dependent variable Y (measured as a

dichotomous or categorical variable---nominal or

ordinal level) using one or more predictor

variables that are continuous or categorical

(ratio, interval, ordinal, or nominal levels)! - For example, we could use multiple logistic

regression to predict the gender of a person

using several predictor variables such as

laziness, pig-headedness, booze consumption, and

number of burps a person does in a day.

Logistic Regression 2

- On a serious note, logistic regression is used in

medical research to formulate models about

variables that predict whether a tumor is likely

to be cancerous or benign, what variables predict

whether a heart attack or stroke survivor is

likely to have a subsequent heart attack or

stroke. - In social science, logistic regression has been

used to develop models that predict the odds that

convicts will recidivate or not which variables

predict if couples will get divorced or not

what variables predict whether people will vote

for a certain party or not what variables

predict if a consumer will purchase a product or

not, etc., etc., etc.

Principles behind Logistic Regression

- In linear regression, we predict Y using a

combination of each predictor variable multiplied

by its respective regression coefficient as

illustrated in the formula - With logistic regression, instead of predicting

the value of Y from one or more predictors, we

predict the probability of Y occurring given

certain values of the predictor variables using

the following formula...

Y a b1X1 b2X2 . bnXn e

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Principles of Logistic Regression 2

- Despite similarities in the underlying equations,

we cannot apply linear regression directly to a

situation where the outcome variable is

dichotomous. - One of the assumptions of linear regression is

that the relationship between the variables is

linear. When the outcome variable is dichotomous

this assumption is not tenable. - One way to circumvent this problem is to

transform the data using the logarithmic

transformationa modification of the data which

as the effect of expressing a non-linear

relationship between variables in a linear way.

Principles of Logistic Regression 3

- Logistic regression expresses the multiple linear

regression equation in logarithmic terms and

resolves the violation of the linearity

assumption. - The resulting value from the equation is a

probability that varies from 0 to 1. A value

close to 0 means that Y is very unlikely and a

value close to 1 means that Y is very likely. . - Each predictor variable in logistic regression

has its own coefficient. The logistic regression

coefficients are estimated using the

maximum-likliihood methodwhich selects

coefficients that make the observed data values

most likely to have occurred. This is the way

that SPSS optimizes the fit of the logistic

regression model.

Logistic Regression A Research Example

- A researcher interested in childhood

socialization wants to identify variables that

predict a childs understanding of social display

norms or rules (an understanding of how to behave

in social situations among children). - The researcher suspects that the childs age and

empathy skills (ability to appreciated the

thoughts and feelings of others), are important

predictors of the childs ability to follow

social display norms. - The outcome variable (Y) is the childs

possession of social display norms (Did the child

pass the social display norm test Yes/No?).

The first predictor variable (X1) is the

possession of empathy (Did the child pass the

empathy test Yes/No?). The second predictor

variable (X2) is the childs age in month (a

continuousinterval or ratio..variable).

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