1. LOGISTIC REGRESSION 1

2. BINARY LOGISTIC REGRESSSION (BLR)2

3. Literature
Applied logistic regression /Hosmer, Lemeshow (1989,2000,375 p.), Regression models for Categorical and Limited Dependent Data, /Scott Long(1997,296 p.), Logistic regression :a primer /Fred C. Pampel (2000,85 p.). Categorical Data Analysis/Agresti (2002,710 p.)
In Czech Řeháková-Nebojte se logistické regrese (Soc. časopis 4: )
LR in SPSS-Discovering statistics using SPSS for Windows :advanced techniques for the beginner /Andy Field (2000,2005,2009) and Norusis

4. Assumptions, variables
Dependent variable
a) binary (binary logistic regression) - todazy
b) ordinl (ordinal regression) - later
c) nominal (polytomous logistic regression) – later
Ind. variables: all types
Close technique: diskriminant analysis (more assumptions for DA, normality of ind. vars)

5. Binary logistic reg Model Probability Odd Odds ratio
Logit-natural logarithm of odds
Equation for binary log reg and back transformations

6. Equation, ind. vars interactions
Ind. vars- binary or nominal: use dummy (SPSS will do it for us)- lats category=reference category)
interaction-see linear regression

7. Basic questions in BLR
Does the model fit to the data? (LR: F-test and R2) a (BLR: pseudo R2 and LR test or Hosmer-Lemeshow test)
Evaluate importance and stat. significance of ind. vars (LR: t-testy and beta coeffs, BLR: Wald test and standardized coeffs)
Does my data fulfill ? (LR: linear relationship between ind and dep. vars, LR: relationship between ind vars and logit)

8. Estimation No usage of OLS
Basic technique: : ML (see also loglinear models, structural equation modelling etc.)
Iterative solution, more steps, impossible to solve without computer

9. Example Usage of Inet - WIP 2006
Intro to data set, selection of vars and exploration

10. BLR in SPSS Equation, Wald’s tests
menu-Analyze-Regression-Binary Logistic

11. Automated inclusion of vars
forward (1)
backward (2)
a) LR (likelihood-ratio) – based on overall test
b) Wald – based on partial test
c ) conditional-simpler version of LR,
6 combinations (1 or 2 vs a)-c))
Reco: use forward and LR or conditional

12. Menu SPSS Categorical-define nominal variables and reference category
Save
residuals and influentials
Hosmer-Lemeshow test
Classification Plot

13. Syntax LOGISTIC REGRESSION VAR=inet /METHOD=ENTER age edu /CLASSPLOT
/PRINT=GOODFIT CI(95)
/CRITERIA PIN(.05) POUT(.10) ITERATE(20) CUT(.5) .

14. Outputs Estimates (Variables in the Equation)
Interpretation of coeff: Change of logit if ind. var. increase by one unit (continuous ind. var) or in comparison with reference category (dummy or binary vars)
exp(B): change in odds if ind. var increase by one unit (if the scale is long use more than one unit, e.g. 10, 100, 1000)

15. Other outputs Wald test
CI for exp(B) -95 % confindence interval for exp(B)
LR tests in table Changes of Goodness-of-Fit:
Model-comparison of our model and model including only interpcept
Block-changes in blocks
Step-changes in Steps if more models are fitted

16. Pseudo R2 Close to (coeff of determination in LR
Can not be interpreted as explained variance (dep. var. is binary)
More formulae exists
Cox and Snell R2- range (0;1) (never achive 1)
Nagelkerke R2- modifief Cox and Snell (can achieve 1)
Mc Fadden- R2- range (0;1) (never achive 1)
The most frequently used is Nagelkerke R2

17. Logistic regression - outputs
Classification table – percentage of correctly classified cases
Histogram of estimated probabilities

18. Probabilty curve in BLR
How to prepare this curve?
Tool in MS Excel

19. Reco for publishing Necessity to differentiate logits, odds
Keep in mind which categories are compared
Coeffs, standardized coeffs
LR test, Wald’s tets, Hosmer Lemeshow test, pseud R2 (mostly Nagelkerke)
It is good to publish classification table or only percentage of correctly classified cases

20. POLYTOMOUS LOGISTIC REGRESSION (PLR)20

21. PLR Dep. var. nominal More equations
Comparison with the last category of dep. var.
menu-Analyze-Regression-Multinomial Logistic

22. SPSS- options Categorical vs. Covariate Statistics Clasification Table
Model
Ind. vars and interactions
Predicted category
Options – transformations

23. Syntax
NOMREG
election BY gender WITH rightor libaut astat intaln extaln anomie age edyrs
/CRITERIA = CIN(95) DELTA(0) MXITER(100) MXSTEP(5) LCONVERGE(0)
PCONVERGE(1.0E-6) SINGULAR(1.0E-8)
/MODEL
/INTERCEPT = INCLUDE
/PRINT = CLASSTABLE FIT PARAMETER SUMMARY LRT .

24. ORDINAL REGRESSION 24

25. Předpoklady a proměnné
One equation with tresholds
Necessary to test whether lines are paralel (if not use PLR)

26. Syntax PLUM q30crec BY q36rec
/CRITERIA = CIN(95) DELTA(0) LCONVERGE(0) MXITER(100) MXSTEP(5)
PCONVERGE(1.0E-6) SINGULAR(1.0E-8)
/LINK = LOGIT
/PRINT = CELLINFO FIT PARAMETER SUMMARY TPARALLEL .
*PLUM-PoLytomous Universal Model (SPSS 10)

27. Ordinal regression – outputs
Estimates (Variables in the Equation)
Interpretation of coeffs-change in logit if ind. var. Increaseby 1 unit (cont. vars.) or in comparison with reference category (dummy or binary vars); use exp(B)-meaning: change in odd (for higher category in comparison with lower one)

28. Pseudo R2 Cox and Snell R2- range (0;1) (never achive 1)
Nagelkerke R2- modifief Cox and Snell (can achieve 1)
Mc Fadden- R2- range (0;1) (never achive 1)

29. CLOSE TECHNIQUES 29

30. Close techniques Discrimination analysis Loglinear analysis
Logit analysis
Classification and regression trees
Following procedures – ROC curves