Weighted Logistic Regression in R, SPSS, Stata

In R:

We will use mtcars dataset to illustrate.  (R version 2.5.1)

> data(mtcars)
> mtcars <- as.data.frame(mtcars)
> mtcars$p <- runif(nrow(mtcars)) # create weights
> mtcars2 <- mtcars[c("am", "hp", "wt", "p")]
> head(mtcars2)
                  am  hp    wt         p
Mazda RX4          1 110 2.620 0.8901532
Mazda RX4 Wag      1 110 2.875 0.4601596
Datsun 710         1  93 2.320 0.9779983
Hornet 4 Drive     0 110 3.215 0.6889322
Hornet Sportabout  0 175 3.440 0.3856835
Valiant            0 105 3.460 0.1209667


> write.table(mtcars2, "mtcars.txt")
> glm(am ~ hp + wt, weights = p, data =mtcars2, family = binomial("logit"))

Call:  glm(formula = am ~ hp + wt, family = binomial("logit"), data = a, weights = p)

Coefficients:
(Intercept)           hp           wt  
   33.88418      0.04686    -13.21937  

Degrees of Freedom: 31 Total (i.e. Null);  29 Residual
Null Deviance:      23.53 
Residual Deviance: 3.21         AIC: 7.49 
Warning message:
In eval(expr, envir, enclos) : non-integer #successes in a binomial glm!

In SPSS: 

Read the mtcat.txt in SPSS (notice that first column name is blank, so give it a name. Check if the data is read properly.) (SPSS version 20)

1. First set "p" as weights. Go to Analyze > Complex samples > Prepare for Analysis > create a plan file in c:\ directory > give a name, say, glmplan > add "p" variable as Sample weight > choose sampling with replacement (WR) with FPC > finish.

2. Use "p" weights in logistic regression from complex samples. Select Analyze > Complex samples > Logistic regression. Here are the syntax with all the specifications chosen.


* Complex Samples Logistic Regression.
CSLOGISTIC  am(LOW) WITH wt hp
  /PLAN FILE='C:\glmplan.csaplan' 
  /MODEL wt hp
  /INTERCEPT INCLUDE=YES SHOW=YES
  /STATISTICS PARAMETER EXP SE CINTERVAL TTEST DEFF DEFFSQRT
  /TEST TYPE=F PADJUST=LSD
  /ODDSRATIOS COVARIATE=[wt(1)]
  /ODDSRATIOS COVARIATE=[hp(1)]
  /MISSING CLASSMISSING=EXCLUDE
  /CRITERIA MXITER=10000 MXSTEP=5 PCONVERGE=[1E-006 RELATIVE] LCONVERGE=[0] CHKSEP=20 CILEVEL=95
  /PRINT SUMMARY CLASSTABLE COVB CORB VARIABLEINFO SAMPLEINFO.


Parameter estimates

Am	par	B	SE
	Intercept	33.884	16.60
1	Wt	-13.219	6.97
	Hp	0.047	0.017

Dependent Variable: am (reference category = 0) Model: (Intercept), wt, hp

Save the SPSS file in Stata (8+) dta format

In Stata:

Read the dataset in Stata first. (Stata version 11)
. use "C:\mtcars.dta", clear
Then use logit or logistic or glm command

. xi: glm am hp wt [pw = p], fam(bin)
. xi: logistic am hp wt [pw = p] //(reports odds ratio)

. xi: logit am hp wt [pw = p]

Iteration 0:   log pseudolikelihood = -11.765859  
Iteration 1:   log pseudolikelihood = -2.6460228  
Iteration 2:   log pseudolikelihood = -1.9094795  
Iteration 3:   log pseudolikelihood = -1.6099406  
Iteration 4:   log pseudolikelihood = -1.6051509  
Iteration 5:   log pseudolikelihood = -1.6051144  
Iteration 6:   log pseudolikelihood = -1.6051144  

Logistic regression                               Number of obs   =         32
                                                  Wald chi2(2)    =       9.10
                                                  Prob > chi2     =     0.0106
Log pseudolikelihood = -1.6051144                 Pseudo R2       =     0.8636

------------------------------------------------------------------------------
             |               Robust
          am |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          hp |   .0468581   .0169369     2.77   0.006     .0136623    .0800539
          wt |  -13.21937    5.96723    -2.22   0.027    -24.91492    -1.52381
       _cons |   33.88418   16.59486     2.04   0.041     1.358857     66.4095
------------------------------------------------------------------------------
Note: 3 failures and 1 success completely determined.