Psychology 513: Advanced Research Methods

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Psychology 513 Advanced Research Methods

• Logistic Regression

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Overview

• Continuous predictor(s) dichotomous criterion
• Can also handle categorical predictors
• OLS regression would give somewhat similar
  results, although probabilities might exceed 0 or
  1 logit model solves this and other problems

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Overview (cont.)

• Transform our dichotomous variable
• Convert probability to odds and then to log odds
  now our DV is a linear function of our
  predictor
• Logit transformation

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Overview (cont.)

• Fits an s-shaped curve (sigmoidal) transforms
  values into probabilities
• Uses maximum likelihood estimation (as opposed to
  least squares)

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Example Peng, Lee, Ingersoll (2002)

• Remedial reading and sex of student

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Example (cont.)

• Logit(Y) a bX
• Logit(Y) ln(odds) lnp/(1-p)
• Where p p(outcome of interest)
• The beta weight reflects the rate of change in
  log odds as X changes

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Example with Two Predictors

• Predict recommendations for remedial reading
  based on reading score (X1) and sex (X2)
• Logit(Y) 0.53 - 0.026X1 0.648X2
• Reading score negatively associated with
  recommendation sex positively associated with
  recommendation

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Example with Two Predictors
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Evaluating the Overall Model

• Compares model to intercept-only model
• Likelihood ratio test
• Score test
• Wald test
• Goodness-of-fit statistics
• Null is that the model fits well

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Recommendations

• Include all of the following
• 1. Overall evaluation of the model
• 2. Tests of individual predictors
• 3. Goodness-of-fit statistics
• 4. Assessment of predicted probabilities
• Note Be aware of possible differences due to
  statistical software