R: mlogit error on data - "system is exactly singular"

Question

So I have data from a randomized blind trial of 1mg of nicotine gum on dual n-back working memory scores; I analyzed them as usual with a t-test and found a small increase in means but a large increase in standard deviations on a f-test! Strange. I also have data for each day on mood/productivity that day on a 1-5 scale.

I wondered: is nicotine following an inverse U-curve, where it causes higher scores on the worser days (1-3) and lower scores on the better days (3-5)? I look around and it seems I want a multinomial logistic regression comparing the placebo & active days.

I enter the data & load mlogit:

nicotine <- read.table(stdin(),header=TRUE)
day      active mp score
20120824 1      3  35.2
20120827 0      5  37.2
20120828 0      3  37.6
20120830 1      3  37.75
20120831 1      2  37.75
20120902 0      2  36.0
20120905 0      5  36.0
20120906 1      5  37.25
20120910 0      5  49.2
20120911 1      3  36.8
20120912 0      3  44.6
20120913 0      5  38.4
20120915 0      5  43.8
20120916 0      2  39.6
20120918 0      3  49.6
20120919 0      4  38.4
20120923 0      5  36.2
20120924 0      5  45.4
20120925 1      3  43.8
20120926 0      4  36.4
20120929 1      3  43.8
20120930 1      3  36.0
20121001 1      3  46.0
20121002 0      4  45.0
20121008 0      2  34.6
20121009 1      3  45.2
20121012 0      5  37.8
20121013 0      4  37.2
20121016 0      4  40.2
20121020 1      3  39.0
20121021 0      3  41.2
20121022 0      3  42.2
20121024 0      5  40.4
20121029 1      2  41.4
20121031 1      3  38.4
20121101 1      5  43.8
20121102 0      3  48.2
20121103 1      5  40.6

library(mlogit)
Nicotine <- mlogit.data(nicotine,shape="wide", choice="mp")
mlogit(score ~ (active + mp)^2, Nicotine)
Error in solve.default(H, g[!fixed]) : 
  Lapack routine dgesv: system is exactly singular
Calls: mlogit ... mlogit.optim -> as.vector -> solve -> solve.default

The error also happens even with the simplest call I can think of:

mlogit(score ~ active, Nicotine)
Error in solve.default(H, g[!fixed]) : 
  Lapack routine dgesv: system is exactly singular
Calls: mlogit ... mlogit.optim -> as.vector -> solve -> solve.default

Reading the documentation for mlogit didn't much help, and look at the other questions having the same error, they're different enough I can't tell whether they apply or not.

Thank you for your assistance.

Answer 1

You don't want multinomial logit as your dependent variable is a score that is nearly continuous. I would start by plotting the data e.g. with

with(nicotine, stripchart(jitter(active)~score, vertical = TRUE))

which doesn't reveal any obvious pattern.

Then you could look at a linear model:

m1 <- with(nicotine, lm(score~as.factor(active)))
summary(m1)

(this is equivalent to the t-test you ran) which shows a small and nonsignificant difference. Plotting m1 doesn't reveal anything particularly interesting to my eyes, either. You say you found large differences in variances but

with(nicotine, sd(score[active == 1]))
with(nicotine, sd(score[active == 0]))

shows the difference to be not all that large (and the stripchart shown above agrees).

Then you could add mp to the model:

m2 <- with(nicotine, lm(score~as.factor(active) + mp))
summary(m2)

which also shows only very small differences and a miniscule $R^2$

There's probably other things you could do, but it looks like there is not much to find here.