# Weights in IPSW (inverse propensity score weighting) too high?

I used a logistic regression on a variable indicating whether a person of an address-dataset took part in a survey (1), or not (0). I extracted the probabilities of each person to participate and calculated the inverse-probability (hence the name of the weighting method - inverse propensity score weighting).

What irritates me, is, that my smallest survey-weight is 1.901. I expected the smallest survey weight to at least be below "1".

I hope somebody can help me and either find out where i made a mistake, or assure me, that i´m on the right track. Any help is greatly appreciated! Thank you!

#Calculate logistic regression
glm2<-glm(indicator ~ var1 + varx,family=binomial,data=sampleframe)

#extract inverse probability of every case
sampleframe$weight<-glm2$fitted^-1

#combine the survey-weight to the survey-data
surveydata<-left_join(surveydata,sampleframe, by="ID")

#diagnostics:
#summary of the weights for the complete sampleframe
Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
1.901   2.810   3.247   3.616   3.836  12.070

#summary of the survey-weights of the participants
Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
1.925   2.686   3.078   3.308   3.502  12.070

#comparison of mean-weight for participants (1) / non-participants (0)
indicator weight.mean
0    3.755967
1    3.295854

• If the probability is less than 1, then the inverse probability must by definition be greater than 1.... – Hong Ooi Feb 18 '15 at 15:38

## 1 Answer

Your predicted probabilities from the logistic regression model, $\pi_i$ will return values between 0 and 1: $0<\pi_i<1$. As a result $1<1/\pi_i< \infty.$ Your inverse weights will never be less than 1. The smallest weight of 1.901 corresponds to a predicted probability of $\pi_i=0.5260389.$ Why were you expecting something different?

• Hi, and thank you for your answer. Of course you and Hong Ooi are right. I somehow thought i forgot a further step where i transform the weight to be smaller. I found a paper that said, the inverse response probabilities as weights would be divided through some constant value "in order to equate the sample size of the weighted dataset with the original sample size". They didn´t explain it further. Perhaps i should take the n of the sample and divide it through n' of the weighted dataset. – SEMson Feb 19 '15 at 12:41