Logistic Regression

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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.

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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.

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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.

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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.

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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).