# 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

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?