Worse than the bugs was the lack of proper scriptability. Pointing and clicking  loses its appeal when you need to run the same model on 12 different datasets, or when you are looking at three variants of the same model and 10 recodes of the same variable. Throw in the desire semi-automatically re-compile the findings from these exercises into two nice tables for inclusion in again and again after finding yet another problem with a model, and you will agree that any  piece of software that is not scriptable is pretty useless for scientists.

MLwiN’s command language was unreliable and woefully underdocumented, and everything was a pain. So I embraced xtmixed when it came along with Stata 9/10, which solved all of these problems.

runmlwin presentation (pdf)

But xtmixed is slow with large datsets/complex models. It relies on quadrature, which is exact but computationally intensive. MLwiN works with approximations of the likelihood function (quick and dirty) or MCMC (strictly speaking a Bayesian approach, but people don’t ask to many questions because it tends to be faster than quadrature). Moreover, MLwiN can run a lot of fancy models that xtmixed cannot, because it is a highly specialised program that has been around for a very long time.

Enter the good people over at the Centre for Multilevel Modelling at Bristol, who have come up with runmlwin, an ado that essentially makes the functionality of MLwiN available as a Stata command, postestimation analysis and all. Can’t wait to see if this works with Linux, wine and my ancient binaries, too.

One common problem with this type of analysis is that not all municipalities are created equal. There is a surprisingly large number of flyspeck villages with only a few dozen voters on, whereas the state’s capital boasts more than 140,000 registered voters. Most places are somewhere in between. Having many small municipalities in the regression feels wrong for at least two reasons. First, small-scale changes of political preferences in tiny electorates will result in relatively large percentage changes. Second, the behaviour of a relatively large number of voters who happen to live in a small number of relatively large municipalities will be grossly underrepresented, i.e. the countryside will drive the results.

My PhD supervisor, who did a lot of this stuff in his time, used to weigh municipalities by the size of their electorates to deal with these problems. But this would lead to pretty extreme weights in my case. Moreover, while voters bring about electoral results, I really don’t want to introduce claims about individual behaviour through the back door.

My next idea was to weigh municipalities by the square root of the size their electorates. Why? In a sense, the observed behaviour is like a sample from the underlying distribution of preferences, and the reliability of this estimate is proportional to the square root of the number of people in a given community. But even taking the square root left me with weights that were quite extreme, and the concern regarding the level of analysis still applied.

Then I realised that instead of weighing by size, I could simply include the size of the electorate as an additional independent variable to correct for potential bias. But this still left me exposed to the danger of extreme outliers (think small, poor, rural communities where the number of Green voters goes up from one to four, a whopping 300 per cent increase) playing havoc with my analysis. So I began reading up on robust regression and its various implementations in Stata.

The basic idea of robust regression is that real data are more likely than not a mixture of (at least) two mechanisms: the “true model” whose coefficients we want to estimate one the one hand, and some other process(es) that contaminate the data on the other. If these contaminating data points are far away from the multivariate mean of the x-Variables (outliers) and deviate substantially from the true regression line, they will bias the estimates.

Robust regression estimators are able to deal with a high degree of contamination, i.e. they can recover the true parameters even if there are many outliers amongst the data points. The downside is that the older generation of robust estimators also have a low efficiency (the estimates are unbiased but have a much higher variance than regular OLS-estimates).

A number of newer (post-1980) estimators, however, are less affected by this problem. One particular promising approach is the MM estimator, that has been implemented in Stata ados by Veradi/Croux (MMregress) and by Ben Jann (robreg mm). Jann’s ado seems to be faster and plays nicely with his esttab/estout package, so I went with that.

The MM estimator works basically by identifying outliers and weighing them down, so it amounts to a particularly sophisticated case of weighted least squares. Using the defaults, MM claims to have 85 per cent of the efficiency of OLS while being able to deal with up to 50 per cent contamination. As you can see in the table, the MM estimates deviate somewhat from their OLS counterparts. The difference is most pronounced for the effect of tax receipts (hekst).

robreg mm has an option to store the optimal weights. I ran OLS again using these weights (column 3), thereby recovering the MM estimates and demonstrating that MM is really just weighted least squares (standard errors (which are not very relevant here) differ, because robreg uses the robust variance estimator). This is fascinating stuff, and I’m looking forward to a forthcoming book by Jann and Veradi on robust regression in Stata (to be published by Stata Press in 2012).

                     OLS              MM            WLS  

greenpct2006        0.193***        0.329***        0.329***
                 (0.0349)        (0.0592)        (0.0278)   

hekst               0.311***        0.634***        0.634***
                 (0.0894)         (0.124)        (0.0688)   

senioren          -0.0744***       -0.100***       -0.100***
                 (0.0131)        (0.0149)       (0.00994)   

kregvoters11      -0.0125        -0.00844        -0.00844
                 (0.0146)       (0.00669)       (0.00982)   

kbevdichte         -0.433        -0.00750        -0.00750
                  (0.464)         (0.330)         (0.326)   

uni                 1.258           0.816           0.816
                  (1.695)         (0.765)         (1.137)   

lnunidist          -0.418**        -0.372**        -0.372***
                  (0.127)         (0.113)        (0.0918)   

_cons               8.232***        7.078***        7.078***
                  (0.627)         (0.663)         (0.461)

Whose afraid of whom?

cii 1043 round(1043*.41)
cii 1043 round(1043*.366)

set obs 5
gen threat = _n
lab def threat 1 "right-wingers" 2 "islamists" 3 "left-wingers" 4 "other" 5 "no threat"
lab val threat threat

gen number = round(1043* 0.41) in 1
replace number = round(1043* 0.366) in 2
replace number = round(1043* 0.056) in 3
replace number = round(1043* 0.038) in 4
replace number = round(1043* 0.13) in 5
expand number

mlogit threat,base(5)

test [right_wingers]_cons = [islamists]_cons

local trials = 10000
foreach v of newlist s1-s`trials' {
qui gen `v' = .
}

mata:
probs =(.388,.388,.056,.038,.13)
st_view(X.,.,"s1-s`trials'",)
X[.,.] = rdiscrete(1043,`trials',probs)
end

local excess = 0

forvalues sample = 1/`trials' {
qui tab s`sample' if s`sample' == 1
local rw = r(N)
qui tab s`sample' if s`sample' == 2
local isl = r(N)
if (`rw' / 1043 * 100) - (`isl' / 1043 * 100) >=4.4 local excess = `excess' +1
}

display "Difference >=4.4 in `excess' of `trials' samples"

CTAN lists a lot of packages and frameworks for posters, but I found most of them too heavy/compl

Political Geography Conference Poster

ex. I don’t create a lot of conference posters and did not want to spend ages putting a few words and graphs on a sheet of glossy paper. At the end of the day, I decided to give beamerp

oster a spin. Beamerposter is an add-on that transforms my favourite presentation package into a poster printing machine. I did not really like the default themes, but Rob Hyndman has created a very alternative nice template that I adapted slightly.

I rather like the result and will go back to the package for the next poster.

rmultinom(1,1000,c(.1,.7,.2,.1))

gives me a vector of random numbers from a multinomial distribution with outcomes 1, 2, 3, and 4, where the probability of observing a ’1′ is 10 percent, the probability of observing a ’2′ is 70 per cent, and so on. But I could not find an equivalent function in Stata. Generating artificial data in R is not very elegant, so I kept digging and found a solution in section M-5 of the Mata handbook. Hidden in the entry on runiform is a reference to rdiscrete(r,c,p), a Mata function which generates a r*c matrix of draws from a multinomial distribution defined by a vector p of probabilities.

That leaves but one question: Is wrapping a handful of lines around a Mata call to replace a non-existent Stata function more elegant than calling an external program?

Marginal Effects at the Mean vs Average Marginal Effects

The first is that in the past when studying the implications from nonlinear (i.e. logit) models, many people including me used to analyse “marginal effects at the margin”. In short, this boils down to holding most  independent vars constant at their grand means/modes while plugging a range of hopefully relevant values for one or two focal variables into the equation.  This approach, which is known as analysing marginal effects at the mean, is easier to understand than to explain but can result in highly unrealistic scenarios if your independent variables are highly correlated (think of holding age constant while varying pensioner/non-pensioner status).

Therefore, looking at average marginal effects might make more sense. These are calculated by varying the focal variable while holding everything else at their variables. This is was the margins command does by default. Michael Norman Mitchell has a post that clearly illustrates the differences between the two approaches to the estimation of margins.   Moreover, there is an older article by Tamás Bartus on his margeff command that is also quite instructive.

Dubious Confidence Intervals

But one problem remains: margins uses a normal approximation for calculating confidence intervals. As a result, after estimating a model for categorical dependent variables, you might end up with a CI for your margins that includes zero, which obviously does not make much sense. Roger Newson seems to know how to get around this issue, but I haven’t tested this approach yet.

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