help with the logistic formula using nlme/nlmer

Dear Hans,

I'd rather use a gamm with a penalized regression spline for
total.hours.worked with a small basis for the smoother (k = 3 of k = 4).

Best regards,

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

2015-06-08 15:07 GMT+02:00 Hans Ekbrand <hans.ekbrand at gmail.com>:

Dear list,

I model the effect of child labour on the childs probability of being
in school. The data comes from 22 countries. Countries have different
means on the outcome variable, ie. the probability is in school is to
a large part determined on in which country the child resides. The
sample includes only children aged 7-14 years.

Child labour is a numerical covariate measured in hours, being in
school is binary variable, age is a numerical covariate, measured in
years.

Data is available here: http://hansekbrand.se/code/cl.df.RData

str(cl.df)

'data.frame':   345321 obs. of  8 variables:
 $ country           : Factor w/ 23 levels "Armenia","Burkina Faso",..: 1
1 1 1 1 1 1 1 1 1 ...
 $ areaID            : Factor w/ 14584 levels "Armenia.1","Armenia.10",..:
3 3 3 3 3 3 2 2 2 2 ...
 $ school            : Factor w/ 2 levels "No","Yes": 2 2 2 2 2 2 2 2 2 2
...
 $ age               : num  9 10 8 11 14 10 12 10 14 12 ...
 $ total.hours.worked: num  1 1 1 0 1 0 0 0 0 0 ...
 $ Chorehours        : num  1 1 1 0 1 0 0 0 0 0 ...
 $ Chwkhours         : num  0 0 0 0 0 0 0 0 0 0 ...
 $ Chothwkhours      : num  0 0 0 0 0 0 0 0 0 0 ...

The distribution of child labour, which is indicated by the variable
total.hours.worked, has a positive skew.

quantile(cl.df$total.hours.worked, probs = seq(from = 0, to = 1, by =

0.1))
  0%  10%  20%  30%  40%  50%  60%  70%  80%  90% 100%
   0    0    0    0    3    5    7   10   14   28  133

I have manually defined classes for this variable,

library(car)
cl.df$hours.class <- recode(cl.df$total.hours.worked, recodes = ("lo:7=1;
 7:14=2; 14:21=3; 21:28=4; 28:35=5; 35:42=6; 42:49=7; 49:56=8; 56:63=9;
 63:hi='more than ten'"), as.factor.result=TRUE)

and used them like this:

fm1 <- glmer(school ~ age + hours.class + (1|country) + (1|areaID), data =
cl.df, family = binomial)

this works, but I would prefer to fit a non-linear regression with a
polynomal form instead. I think a simple exponential function would
work.

E.g.

fm1 <- glmer(school ~ age + I(total.hours.worked^2) + (1|country) +
(1|areaID), data = cl.df, family = binomial)

However, I *think* nlmer() could be used to find the optimal number
instead of "2" here. But I don't know how to do that. I have searched
the archive, but found rather few posts concerning nlmer(), so any
help is much appreciated.

If you can solve the problem with nlme() or anything else for that
matter, that's perfectly fine, I'm used to lme4, but I'm happy to
learn new stuff.

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