Hi,
i am trying to learn something about multilevel analysis using a great
"Discovering statistics using R". I constructed some sample data and then
tried to fit a model. Generally model fits well, however when trying to fit
the same model using z-score (standarizded) variables i got an error:


Error in lme.formula(z_wyn ~ z_IQ + Kasa, data = la, random = ~z_IQ |  :
  nlminb problem, convergence error code = 1
  message = iteration limit reached without convergence (10)


Below i attach all the code required to reproduce. My question is : is it a
bug or a feature, in other words: is it normal for a model not to converge
using z-scores ? If so, how to estimate standarized coefficents ? Or maybe
i messed up something to begin with?


 Here is what i do:
                       library(nlme)

                       # I am creating random data
                       # df of 900 rows
                       la <- data.frame(1:900)

                       # municipality: the variable i want to base my
multilevel analysis on
                       la$municipality[1:300] <- "Warszawa" # name of
municipality: "Warsaw"
                       la$municipality[301:600] <- "Płock" #
                       la$municipality[601:900] <- "Gniezno" #

                       # money that each municipality spends on schools
(per student)
                       la$money_per_municipality[1:300] <-  500 # name of
municipality: "Warsaw"
                       la$money_per_municipality[301:600] <- 300 #"Płock" #
                        la$money_per_municipality[601:900] <- 200
#"Gniezno" #

                       # In my model, i want to estimate student's
achievments,
                       #so i pick some random data, but I also want to
                       #differentiate between the municipalities

                       la$students_score[la$municipality=="Warszawa"] <-
rnorm(n=nrow(la[la$municipality=="Warszawa",]),mean=33,sd=4)

                       la$students_score[la$municipality=="Płock"] <-
rnorm(n=nrow(la[la$municipality=="Płock",]),mean=22,sd=4)

                       la$students_score[la$municipality=="Gniezno"]
<-rnorm(n=nrow(la[la$municipality=="Gniezno",]),mean=5,sd=4)


                       ### I assume IQ ~ achievement relation 2x + stderr
                       la$IQ <- la$students_score * 2 +
rnorm(n=nrow(la),mean=0,sd=30)

                       with(la,cor(students_score,IQ))
                       #### [1] 0.6202439
                       ## convert factor/string to integer:
                       la$mun <- as.integer(factor(la$municipality))

                       ### Z SCORES for IQ and achievements
                       la$z_IQ <- (la$IQ-mean(la$IQ))/sd(la$IQ)
                       la$z_sscore <-
(la$students_score-mean(la$students_score))/sd(la$students_score)

                       ## Estimate a model with random slopes based on IQ
for each municipality.
                       ##Again: z_IQ is plain IQ, money_per_municipiality
does not very between municipialities

                       # THIS runs without an error
                       studentModel<- lme(z_sscore ~ IQ +
money_per_municipality, data=la,random=~IQ|mun,method="ML")

                       # THIS causes an error. The only difference is one
variable (z_IQ instead of IQ)
                       studentModel<- lme(z_sscore ~ z_IQ +
money_per_municipality, data=la,random=~z_IQ|mun,method="ML")

Output again:
                       Error in lme.formula(z_sscore ~ z_IQ +
money_per_municipality, data = la,  :
                         nlminb problem, convergence error code = 1
                                            message = iteration limit
reached without convergence (10)



Best,
Mikołaj Hnatiuk, Educational Research Institute, Warsaw, Poland

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