[R-sig-ME] Unstandardizing GLMM Regression Coefficients

[Thierry Onkelinx]

Dear Timothy,

Please don't post in HTML. It makes code unreadable.
Please post code that can be easily reproduced: a simple copy/paste should
work.

You might want to consider a very simple scaling by just using expressing
the variables in another unit (= multiplying by some power of 10). E.g.
kilometers to meters or gram to decagram.

Best regards,

Thierry


ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

2016-01-18 7:52 GMT+01:00 Timothy Lau <timothy.s.lau op gmail.com>:

> Hello,
>
> lme4 mentioned that I should consider rescaling some of my predictor
> variables because of the scale differences:
>
> *fit warnings:*
> *Some predictor variables are on very different scales: consider rescaling*
>
>
>
> I have since been trying to expand Ben Bolker's function:
>
> *#
>
> http://stackoverflow.com/questions/23642111/how-to-unscale-the-coefficients-from-an-lmer-model-fitted-with-a-scaled-respon
> <
> http://stackoverflow.com/questions/23642111/how-to-unscale-the-coefficients-from-an-lmer-model-fitted-with-a-scaled-respon
> >*
> *rescale.coefs <- function(beta,mu,sigma) {*
> *  beta2 <- beta ## inherit names etc.*
> *  beta2[-1] <- sigma[1]*beta[-1]/sigma[-1]*
> *  beta2[1]  <- sigma[1]*beta[1]+mu[1]-sum(beta2[-1]*mu[-1])*
> *  beta2*
> *}*
> *# regular model*
> *m1 <- lm(Illiteracy~.,as.data.frame(state.x77))*
> *b1 <- coef(m1)*
> *# Make a scaled version of the data*
> *ss <- scale(state.x77)*
> *# Scaled coefficients:*
> *m1S <- update(m1,data=as.data.frame(ss))*
> *b1S <- coef(m1S)*
> *# rescaling*
> *icol <- which(colnames(state.x77)=="Illiteracy")*
> *p.order <- c(icol,(1:ncol(state.x77))[-icol])*
> *m <- colMeans(state.x77)[p.order]*
> *s <- apply(state.x77,2,sd)[p.order]*
> *all.equal(b1,rescale.coefs(b1S,m,s))  ## TRUE*
>
>
>
> to work with GLMM models (e.g., count data) that can't have the outcome
> standardized, only the predictors:
> *# function assumes scaled data is within model; no NA's and only used
> variables are in orig.data*
> *unscale.coef.mer <- function(model, orig.data) {*
> *  require(lme4)*
> *  ran.ef <- as.character(attr(attr(model op frame,
> "terms"),"predvars.random"))[-1:-2] # random effects*
> *  offset <- attr(attr(model op frame, "terms"), "offset")*
> *  scaled.data <- model op frame[,!names(model op frame) %in% c(ran.ef, offset)]
> # the scaled covariate(s) and outcome used in the model*
> *  orig.data <- orig.data[,!names(orig.data) %in% c(ran.ef, offset)]*
> *  beta <- fixef(model) # the fixed effects*
> *  outvar <- names(model op frame)[attr(attr(m3 op frame, "terms"), "response")]
> # the outcoem var. name*
> *  icol <- which(colnames(orig.data) == outvar) # outcome variable column
> number*
> *  p.order <- c(icol, (1:ncol(orig.data))[-icol]) # full list of variable
> names with outcome 1st*
> *  mu <- colMeans(x = orig.data)[p.order] # variable means with outcome
> 1st*
> *  sigma <- apply(X = orig.data, MARGIN = 2, FUN = sd)[p.order] # variable
> SDs with outcome 1st*
> *  beta2 <- beta # inherit names etc.*
> *  beta2[-1] <- sigma[1] * beta[-1] / sigma[-1] # the fixed effects except
> intercept*
> *  beta2[1]  <- sigma[1] * beta[1] + mu[1] - sum(beta2[-1] * mu[-1]) # the
> FE intercept*
> *  return(beta2)*
> *}*
>
>
> ​Could someone help me ​with backing out or unscaling the coefficeints so
> that m2 coef matches m1 even though m2 used the standardized data (example
> data):
> *# warnings due to scaling*
> *m1 <- glmer(formula = awards ~ 1 + write + (1 | cid), family = poisson,
> data = foreign::read.dta(file =
> "http://www.ats.ucla.edu/stat/data/hsbdemo.dta
> <http://www.ats.ucla.edu/stat/data/hsbdemo.dta>"))*
>
> *​# fixed scaling but need to back out coefficients to original scale for
> interpretative reasons​m​2​ <- glmer(formula = awards ~ 1 +
> ​scale(​write​)​ + (1 | cid), family = poisson, data =
> foreign::read.dta(file = "http://www.ats.ucla.edu/stat/data/hsbdemo.dta
> <http://www.ats.ucla.edu/stat/data/hsbdemo.dta>"))*
>
>
>
> Best,
> Timothy
>
>
>
> "The will to win means nothing without the will to prepare."
> http://en.wikipedia.org/wiki/Juma_Ikangaa
>
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>
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