LOGISTIC REGRESSION Flashcards

1
Q

What is logistic regression?

A
  • Logistic regression is used to predict non-continous variables
    • Also known as Logit Analysis
    • Can be multinomial, ordinal or binary.
    • Similar to discriminant analysis (in MANOVA) but differs in terms of assumptions so not interchangeable
  • Logistic regression doesn’t try to predict an outcome score. Rather, it predicts the probability an event will occur given the predictive values.
  • Predicts outcome by creating a variate comprised of the IVs
    • Variate = measure comprised of 2+ variables
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2
Q

What are the advantages of logistic regression?

A
  • Doesn’t require many assumptions to be met
    • Doesn’t require:
      • Normality
      • Linearity
      • Homoescadescity
    • Although they do increase predictive power
  • Can be interpreted in a similar way to multiple regression
  • Forced, Hierachical and stepwise methods all available
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3
Q

What are the disadvantages of logistic regression?

A
  • Still has some assumptions
    • Independence of errors,
    • Linearity of logit,
    • Absence of outliers
  • Need strong theoretical justification for predictors
  • Causality cannot be established
  • Requires large sample size
  • Problems with model overfit/complete separation
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4
Q

What is the odds ratio?

A
  • The odds ratio (ExpB) tells you how a 1 unit change in the predictor will affect the probability of the outcome occuring
    • Ratio = ( odds after unit change) / (original odds)
    • >1 = odds of outcome increase < 1 = odds of outcome decrease
    • If confidence interval crosses 1 the ratio isn’t statistically significant
  • Unadjusted vs Adjusted Odds Ratio:
    • UOR: not adjusted for presence of other predictors
    • AOR: Represents association when other variables are held constant
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5
Q

What are Model Parsimony and Linearity of the Logit?

A
  • Model Parsimony; A parsimonious model is one in which minimal predictor variables that together maximally explain the outcome variable
    • Select and use only those predictors that are likely to explain the outcome
  • Linearity of the Logit; a linear relationship between the continuous predictors and the log transformation of the outcome variable
    • log transformation means that the probabilities remain between 0 and 100%.
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6
Q

What are log likelihood and deviance?

A
  • Log Likelihood is equivalent to the SSR (sum square residuals)
    • Log Likelihood: Compared predicted and actual probability
      • Large value = poor fit, small value = good fit
  • The Deviance score (-2LL) is used to compare model parsimony and to calculate R2
    • Chi-square distribution of log likelihood
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7
Q

What are the different versions of R2 in logistic regression?

A
  • R2 is a measure of variance explained; all are derived from Deviance Stat
    • In log regression cannot simply square R statistic
  • Homer and Lemenshow: Orders data by group and compares to prediction using CHISQ dist
  • Cox and Snell: uses sample size, used by SPSS
    • Neve reaches theoretical max so limited in high end
  • Nagelkerke: moderated Cox and Snell to fix upper limit
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8
Q

What is the Wald Statistic?

A
  • Wald Statistic (z statistic)
    • Logistic regression equivalent of the t statistic)
    • SPSS reports as z2 to get a chisquare distribution
  • Tells us whether the contribution is significant
    • Be cautious; when b is large SE becomes inflated
    • More accurate to add in hierachically and examine change in Likelihood stats
    • Check if CI crosses 0
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9
Q

How is logistic regression accomplished in SPSS?

A
  • Correlate -> Bivariate -> Add all variables
    • Select potential predictors
    • Be careful with negative predictors (cancel out positive predictors)
  • Analyse -> Regression -> Binary Logistic
    • Outcome in Dependent, Predictors in covariate
    • Choose ‘enter’ method (unless hierachical is warranted)
    • If categorical predictor present -> categorical -> move predictor into box
    • Save; group membership
    • Options; Hosmer, CI, Classification
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10
Q

How do you interpret logistic regression output in SPSS?

A
  • Check which cases are included under case processing
  • Block 0; Null hypothesis model
    • Probability without predictors
  • Variables not in equation; shows prediction outside model
  • Block 1; Simultaneous model
    • Omnibus test compares to Block 0 (p<.05 =good predictor)
    • Nagelkerke = variance explained
    • Homer-Lemenshow < .05 = good
    • Exp(B)= odds ratios
  • Contingency tables; Shows how many cases were correctly predicted
  • Classification tables; % correct predicted
    • compare to Null model
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11
Q

How is model parsimony tested in SPSS?

A
  • Model Parsimony; testing during main analysis
    • Add the different predictors in steps
    • Under Categorical; tick change and contrast
    • Under omnibus tests; compare the blocks and rerun only the best model
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12
Q

What are some common problems in logistic regression?

A
  • Overdispersion; the variance is larger than expected from the model
    • Makes SE/CIs too small
    • Caused by violating independence of errors assumption
    • Present if Dispersion Parameter is greater than 1 ( big problem if over 2)
  • Incomplete Information from Predictors;
    • Ideally, you should have some data for every possible combination of predictors (definitely for categorical)
    • Violation causes large SEs
  • Complete Separation; when outcome can be perfectly predicted by 1+ predictor
    • model collapses, large SEs
      *
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