Addiction Research and Theory

February 2009; 17(1): 96–98

Response Commentary

Reply to Stockwell and Kerr

JAMES MCINTOSH1,2

1Economics Department, Concordia University, Montreal, QC, H3G1M8 Canada and2The Danish Centre for Social Research, Copenhagen, Denmark

Introduction

Stockwell and Kerr (2009) refer to the statistical procedure that I use in my paper, McIntosh

(2008), to treat the problem of unobservables as a ‘magical piece of statistical sophistry’.

There is nothing magical or misleading about this; it is a technique which is well established

in the statistics and econometrics literatures.

Unobservable effects are extremely important in the analysis of human behaviour and they

require statistical procedures which can produce reliable parameter estimates when they are

present. In the paper, I noted that how careful or prudent individuals were could effect their

health outcomes but there were no adequate observable measures of this attribute.

The treatment of the missing prudence variable was accomplished by estimating a model

based on a finite set of mixture distributions each one of which represents a type with a type

specific mean.

To see exactly what is involved here let zi be an outcome variable for individual i and

suppose that it has a conditional probability distribution f(zi,�(Xi, pi)), where

E(zi)¼�(Xi, pi) and (Xi, pi) are the vector of regressors which reflect i’s characteristics and

pi is i’s level of prudence. One way of proceeding is to assume a distribution for pi and then

integrate with respect to pi to get an unconditional or average density function. This

procedure is well established and a modern summary of it may be found in Cameron and

Trivedi (2005, Ch 18). Unfortunately, this is a rather restrictive procedure since it does not

allow for the possibility that the level of prudence could affect the degree to which the

outcome variable responds the regressors and it depends on the choice of mixing

distribution. Latent class models discussed in Aitkin and Rubin (1985) and Wedel et al.

(1993) are an attractive alternative which admits this possibility.

Correspondence: J. McIntosh, Economics Department, Concordia University, 1455 de Maisonneuve Blvd. W, Montreal, QC,

H3G1M8, Canada. Tel.: 514 848 2424. E-mail: jamesm@vax2.concordia.ca

ISSN 1606-6359 print/ISSN 1476-7392 online � 2009 Informa Healthcare USA, Inc.

DOI: 10.1080/16066350802582714

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In latent class models the variation in the level of prudence can be captured by a finite

number of discreet values of pi each of which defines a type. Additionally, the responses to

the regression variables are type specific. When there are K types, the latent class procedure

assumes that each type has its own probability distribution with mean �(Xi,�k)

k¼ 1, 2, . . . , K. The model can then be estimated as the mixture distribution whose

probability mass function is

gðziÞ ¼XK

k¼1

�k f ðzi,�ðXi,�kÞÞ ð1Þ

and

XK

k¼1

�k ¼ 1, ð2Þ

where �k is the probability of being type k. The (�, �k) parameter vectors are to be estimated.

K is not usually known but researchers usually find that a small number of mixtures, 2 or 3,

provide a better explanation of the data than a single unmixed model. A special case of the

model, due to Heckman and Singer (1984), allows only the type specific intercept terms, �k0,

to differ across types. That was the procedure used in my article and allows for different

levels prudence across types, but their level of prudence does not affect how they respond to

their characteristics.

Models which allow for unobserved heterogeneity of the form described here are clearly

superior to conventional statistical models in terms of likelihood criteria and provide a richer

and more informative framework for the analysis of medical data.

Stockwell and Kerr do, however, raise two important issues. These are the stability of

drinking habits over time and the issue of causality. They also mention that problems could

arise if occasional drinkers are grouped with abstainers. This is not a problem in my study, as

they acknowledge. Although I use the Statistics Canada categories of regular and occasional

drinkers in Table 1 of the original paper. I make no use of this distinction since it is only the

number of drinks per day consumed on average that represents alcohol use. I also

constructed a variable ‘heavy drinker’ which was, whether the respondent consumed more

than five drinks a day at least twice a week. Given the presence of the actual number of

drinks consumed as a regressor this variable was never significant, so it was not used in the

analysis.

Canadian drinkers do change their habits over time as indicated by the large number of

respondents who claim former drinker status. But are there large number of heavy drinkers

who in later life become occasional drinkers? The answer to this question appears to be no.

Suppose that this were the case and former heavy drinkers react differently to the amount of

alcohol consumed than respondents who were never heavy drinkers. This would generate

a typology with different behaviours with responses to alcohol consumption. In response to

Stockwell and Kerr’s comments on this issue, I tried to estimate models where there were

two types of response to alcohol. No significant increase in the likelihood functions in the

models of self-reported health, heart disease or diabetes were obtained when I allowed the

coefficients of ni and n2i to differ across the two types. Hence, this does not appear to happen.

The issue of stability of drinking habits is also related to the question of which way the

causality runs in the relation between alcohol consumption and the probability of having

heart disease or diabetes. Stockwell and Kerr are much concerned about this and see my

interpretation of the non-linear relation between the current number of drinks that the

Reply to Stockwell and Kerr 97

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respondent reports and having either of the two diseases as being a causal relation as a major

shortcoming in my analysis. They appear to be of the opinion that most sample survey data

is largely uninformative about causality issues.

Fortunately, the CCHS survey asks a question about changes in the respondent’s alcohol

consumption behaviour and the reason why the respondent consumed less alcohol. For

example, in the group of men aged 50–59 years 5.1% reported reducing their alcohol

consumption for various health related reasons. The correlation coefficient between the

reduced alcohol consumption variable and the reported heart disease is small, 0.054, but it is

significant which means that having heart disease could lead to changes in alcohol

consumption and this relation could be causal as well.1 But what is important here is that for

95% of the respondents in this age group drinking behaviour among drinkers has remained

unchanged. For male drinkers the average number of drinks per day at age 30 is 1.67. At

age 60 this has fallen slightly to 1.59 drinks per day, a negligible decline. Thus, alcohol

consumption behaviour has remained remarkably stable over large increases in age for those

who continue to drink.

When I reestimated the model on this male age group having deleted both the drinkers

who report a change in drinking habits as well as former drinkers I obtained very similar

results to those which appeared in the original paper.2 The proportions of males reporting

heart disease start to increase significantly only after age 40, long after drinking habits have

been established. As a result, the case for believing that moderate alcohol consumption can

cause a reduction in the probability of heart disease or diabetes is, in fact, quite compelling.

Declaration of interest: The authors report no conflicts of interest. The authors alone are

responsible for the content and writing of the paper.

Notes

1. The time series econometrics literature on causality clearly demonstrates that causal relations can go inboth directions simultaneously, so that heart disease might cause individuals to drink less in no waydiminishes the probability that moderate alcohol lowers the probability of heart disease.

2. These are �n¼0.234* (0.095) and �ns¼0.010 (0.010).

References

Aitkin M, Rubin DB. 1985. Estimation and hypothesis testing in finite mixture models. Journal of the Royal

Statistical Society, Series B 47:67–75.

Cameron AC, Trivedi PK. 2005. Microeconometrics: Methods and Applications. New York: Cambridge

University Press.

Heckman JJ, Singer B. 1984. A method for minimizing the impact of distributional assumptions in econometric

models for duration data. Econometrica 52(2):271–320.

McIntosh J. 2008. Is alcohol consumption good for you? Results from the 2005 Canadian Community Health

Survey. Addiction Research and Theory 16(6):553–563.

Stockwell T, F Kerr WC. 2009. Is alcohol consumption good for you? Commentary on McIntosh. To appear in

Addiction Research and Theory 17(1):91–95.

Wedel M, Desarbo WS, Bult JR, Ramaswamy V. 1993. A latent class poisson regression model for heterogeneous

count data. Journal of Applied Econometrics 8:397–411.

98 J. McIntosh

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