Lovely Lucid Logistics the analysis and graphic presentation of effects of nominal and metric variab

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Lovely Lucid Logistics the analysis and graphic
presentation of effects of nominal and metric
variables on binary outcomes

• Diana Eugenie Kornbrot
• Blended Learning Unit
• University of Hertfordshire
• d.e.kornbrot_at_herts.ac.uk

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Abstract

• Logistic regression can be used to answer the
  same questions about binary variables that ANOVA
  and ANCOVA answer about metric variables.
• However, SPSS provides much less support for
  logistic regression. The Logistic Regression
  Procedure provides no equivalent of ANOVA Means
  Tables or Profile Plots.
• This presentation shows how to use a combination
  of SPSS Procedures to produce Tables and Graphs
  of predicted logit and probabilities as a
  function of categorical factor and metric
  covariate variables.
• Diagnostics for model fit NOT discussed
• Merits own presentation

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Acknowledgments

• Lia Kvavilashvili
• For all the prospective memory data
• Stimulating theoretical discussion on content
• ESRC Project Grant

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Goals

• Motivate Logistic regression
• Graphic Presentation of Logistic Model Results
• Interpretation much easier from graphs
• Predictions
• Logits and Probabilities as function explanatory
  variables
• Identification of statistically reliable effects
• Factors and Contrasts
• Application to Different Designs
• Explanatory variables 2 or 3 categorical
• Explanatory variables 1 metric, 1 or 2
  categorical
• Recommendations to Users of Logistic Regression
• Recommendations to SPSS

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Why Logistic Analysis?

• Need to analyse binary, i.e. 2 alternative,
  responses
• Errors right, wrong
• Events remembered, forgotten
• Success grant awarded, grant rejected
• patient recovered, or not
• More than 1 categorical variable
• Chi-square not sufficient
• Combination of metric and categorical explanatory
  variables
• Interactions matter

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Why Interpretation of Results is a Problem

• Analysis is on log (odds ratio) or logits
• Lack of intuitive feel for logits
• Lack of intuitive feel for odds ratios for
  non-betters
• Probabilities are more natural?
• Need for Packages SPSS or other
• Cant hand calculate, as no closed form answer
• SPSS Output
• Primary output is in logits
• No directly useful graphics output
• BUT Save permits direct saving of probabilities
  no logits
• ?No confidence levels on probabilities

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Analysis

• Analysis
• GLM framework
• Effects assumed to be linear on logits
• Model Goodness of Fit Test on 2LogLikelihood,
  -2LL
• Model Fitting Procedure
• SPSS uses Wald, other packages use deviance
  -2LL
• Effect of Evauluation Criteria SPSS uses Wald
• On factors and covariates
• On model parameters
• Other Packages Vary, all give Wald as minimum
• JMP, SPSS, SAS, SYSTAT

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Data Example Prospective Memory

• Prospective Memory
• Does person have GOOD prospective memory
• 5 or 6 occasions remembered from 6 opportunities
• Model 1 task(action, event, time), age(4
  categories)
• Model 2 task(action, event, time), age(4),
  intellect
• Presentation Criteria
• Easy to interpret gt Graphics
• Predicted probability and logits
• Estimate of accuracy as part of results
• Tests for explanatory variable effects and
  contrasts

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Model 1 using SPSS menus

• Analyze gt Regression gt Binary Logistic
• Dependent good
• Covariates task(cat)
• age(cat)
• task(cat)age(cat)
• Method Enter
• Categorical task(deviation) age(deviation)
• or task(repeated) age(repeated)
• !!!NOT indicator, the default!!!
• not a lot of people know that!
• Save probabilities, Cooks, deviation
• Options CI for exp(B)

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Model 1 Global Results

• Model 1 task(action, event, time), age(4
  categories)
• Omnibus Test Significant Good
• Model Summary Substantial variance accounted for

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SPSS Model 1 Parameters

• Variable effect not salient
• No effects or standard errors for reference
  (last)
• Wald Estimates of s.e. may not be those that are
  needed?

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SPSS Graphic Representation

• Predicted Probabilities, pre_1
• Directly Available from Save
• Logits can be calculated
• Compute gt Transform
• Lgt ln(pre_1/(1-pre_1)
• NB Most other packages allow direct saving of
  logits
• Graph gt Interactive gt Line plot
• Y axis predicted probability (mean)
• X axis age
• Colour task
• No interactions
• So expect logit plots to be more linear

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SPSS Logit Probability Graphs
Raw probability Logit ??looks more
linear?? Confidence Levels??? NOT in SPSS!!!
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Confidence Levels

• Assume no extra-binomial dispersion
• Asymptotic for logit
• Symmetric about mean(lgt)
• se(lgt)2 1/Noccur - 1/Nnot occur
• Lower Confidence Level, 95, LCL(lgt) mean(lgt)
  -1.96se(lgt)
• Upper Confidence Level, 95, LCL(lgt) mean(lgt)
  1.96se(lgt)
• Asymptotic for probability
• Asymmetric about mean(prob).
• Calculate from lgt CLs
• probability exp(lgt)/1exp(lgt
• LCL(prob) exp(LCL(lgt)0/1exp(LCL(lgt))
• UCL(prob) exp(UCL(lgt)0/1exp(UCL(lgt))
• Use EXCEL, cant customise error bars in SPSS

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EXCEL Logit Probability Graphs
Raw probability Logit Errors are for each group.
So low power for interaction
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Model 2 Using SPSS menus

• Analyze gt Regression gt Binary Logistic
• Dependent good
• Covariates task(cat), age(cat), intellec
• task(cat)age(cat)
• task(cat)intellec
• intellecage(cat)
• task(cat)age(cat)intellec
• Method Enter
• Categorical task(deviation), age(deviation)
• or task(repeated), age(repeated
• Save probabilities, Cooks, deviation
• Options CI for exp(B)

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Model 2 Summary

• OmnibusWhole Model LR chi2(23)82.2, p.0000001
• Various r2 values
• McFadden.36 Cox Snell.37 Nagelkerke.51
• Variable Effects
• Source DF Wald chi2 Wald Prob LR Chi2 LR Prob
• TASK 2 14.03 .000899 29.70 .000000
• AGE 3 3 4.45 .217040 4.96 .174500
• intellect 1 2.87 .089995 6.03 .014101
• TASKAGE 6 6.00 .423621 14.63 .023371
• TASKintellect 2 4.32 .115183 7.73 .021003
• AGEintellect 3 5.00 .171542 7.07 .069614
• TASKAGEintellect 6 10.52 .104480 21.43 .001532
• Comparison of Variable Effects with different
  methods/packages
• Likelihood Ratio shows strong effects intellec
  intellec interactions
• Used JMP-IN even version 3, 5 is better for some
  things
• Wald does NOT show these effect - WORRYING
• Model improvement with intellec chi2(12)33.3,
  p.00087

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Model 2 Probability by Age

• Not very clear!
• Task effect
• Event has lower prob
• Intellect
• Most groups
• Prob increase with intellec
• 3 way interactions
• gt 70, event 61-65 time
• Prob decrease with intellec

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Model 2 Logit by Age

• Bit clearer!
• Task effect
• Event has lower prob
• Intellect
• Most groups
• Prob increase with intellec
• Large 71-75time, 76-80action
• 3 way interactions
• gt 70, event 61-65 time
• Prob decrease with intellec

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Summary Recommendations

• Recommend Logit analyses as a very important tool
• Recommend Graphic displays toimprove
  interpretability
• SPSS provides basic procedure
• Limitations of SPSS
• No direct predicted logit or probability Table or
  Graph Summary
• Poor model diagnostics and power procedures
• No direct group standard errors
• No Maximum Likelihood estimates for explanatory
  variables
• No mixed models
• Other general packages are also DIRE - in
  different ways
• Need simple tools for routine logistic
  applications
• Can SPSS User Groups do anything?

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References

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• Kornbrot, D. E. (2000, 17-20 july 2000). Counting
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  log linear models over ANOVA and correlations.
  Paper presented at the 1st International
  Prospective Memory Conference, Hatfield,
  Hertfordshire, U.K.
• Kvavilashvili, L., Kornbrot , D. E., Mash , V.,
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