# [Commentary] HOW TO MODEL TWO-WAVE PANEL DATA?

Version of Record online: 28 JUN 2008

DOI: 10.1111/j.1360-0443.2008.02259.x

© 2008 The Author. Journal compilation © 2008 Society for the Study of Addiction

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#### How to Cite

NORSTRÖM, T. (2008), [Commentary] HOW TO MODEL TWO-WAVE PANEL DATA?. Addiction, 103: 938–939. doi: 10.1111/j.1360-0443.2008.02259.x

#### Publication History

- Issue online: 28 JUN 2008
- Version of Record online: 28 JUN 2008

- Abstract
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### Keywords:

- Alcohol;
- dichotomization;
- differencing;
- gender roles;
- lagged dependent variable;
- panel data

Several countries have witnessed a steady decline in the last few decades in the male/female ratio of drinking and alcohol-related outcomes. Some studies suggest that this may be due, in part, to changing gender roles resulting in a more masculine drinking pattern among women. However, most research on this topic is based on cross-sectional data with all their well-known limitations as to causal inferences. The study by Kubička & Csémy [1] is therefore a valuable contribution to the field, as its longitudinal approach improves the possibilities for finding non-spurious associations. More specifically, their data comprise a two-wave panel of Prague women interviewed in 1992 and 1997 about their alcohol habits and gender role conceptions. As the authors point out, the two measurements delimit a period with marked societal changes with a potentially great impact on the topics at issue, and the findings indeed suggest a link between women's drinking and their gender role conceptions. Is this a well-founded conclusion? To address that question I will discuss two methodological issues of general interest which the paper brings to the fore.

### Two models for analysing two-wave panel data

Assume that we have the model:

where *Y* is alcohol use, *X* is a gender role variable, and *U* is an unmeasured correlate (e.g. some personality trait) of *Y*. If *U* and *X* are correlated, the estimate of *b* will be biased when the model is estimated on cross-sectional data. Panel data are often regarded as a remedy against such omitted variable bias, and a panacea for drawing causal conclusions. However, the degree to which this is true depends strongly upon how the data are modelled. There are two major approaches for the modelling of two-wave panel data: the lagged dependent variable (LDV) and the first difference (FD) methods. LDV means that *Y _{t}*

_{−1}is included among the explanatory variables in order to control for the initial level of the outcome (this is the method that Kubička & Csémy use). FD means that we analyse the changes between

*t*1 and

*t*2 by regressing Δ

*Y*on Δ

_{t}*X*where Δ

_{t}*Y*=

*Y*−

*Y*

_{t}_{−1}. Which of the two methods should be chosen? There is hardly any consensus (or a shifting consensus) on this matter, but I find the arguments favouring FD more compelling. The main advantage of FD is that it provides a better safeguard against omitted variable bias: if

*U*in the model above is stable across time, the differencing means that it is cancelled out and this source of bias is eliminated. Applying FD means that the effect estimate of

*X*is driven entirely by the temporal variance that is induced by change, and this corresponds to the research topic at issue; the effect of

*changes*in gender roles.

When, instead, LDV is applied the model has the following form (which is basically what Kubička & Csémy estimate):

First, it is evident that the information contained in *X _{t}* is not utilized. Further, the effect estimate of

*X*is more likely to be biased [2] as confounding influences from omitted variables are not differenced out, and may not be controlled adequately by the lagged dependent variable. An obvious and potential downside of FD is the greater risk of type 2 error (not detecting an existing relationship) in cases when few people change in their

*X*-values. The choice between FD and LDV is thus much a trade-off between type 1 and type 2 errors, with FD being the more conservative approach.

Nevertheless, there are certainly proponents of LDV, e.g. Finkel [3], to whom Kubička & Csémy (and many other researchers) refer. However, Finkel also points out the drawback of LDV that measurement errors in *Y _{t}*

_{−1}(which are bound to exist) tend to induce an upward bias of the estimated effect of

*X*. As a remedy, Finkel suggests the incorporation of a measurement error model by using LISREL. This second step is quite demanding and not always possible due to data restrictions, and thus seldom accomplished. One instance in which LDV might be preferable is when

*Y*

_{t}_{−1}has a causal effect on

*Y*. However, whether this is the case is often almost a philosophical question. In most instances the correlation between

_{t}*Y*and

_{t}*Y*

_{t}_{−1}can be seen as a result of stable personality and environmental characteristics. Further, the simulation results reported by Johnson [4] suggested that applying FD when

*Y*

_{t}_{−1}actually has an effect did not bias the estimated estimate of

*X*. Generally, these simulations singled out FD as being superior to LDV (see also Allison [5]).

### Why dichotomize?

The outcome measures of alcohol use are analysed as continuous variables (e.g. frequency and volume), and in addition as dichotomized indicators (using various cut-offs of hazardous drinking, such as ≥96 g alcohol per session). This handling of the outcome is highly commendable, and differs from a practice that is often seen, namely to analyse a continuous variable only in a dichotomized form. Because this practice is so common, it may be worth pointing out its drawbacks.

Dichotomization may be useful and practical in a clinical setting as a basis for a binary decision, e.g. concerning need for treatment or assigning a diagnosis. However, in alcohol epidemiology the situation is different, and a dichotomization of, for example, a problem drinking scale is at odds with contemporary conception of abuse. Problem drinking comes in degrees, rather than being practised by a clearly delineated population group. Often the dichotomization is made without any rationale, with the use of cut-offs that are arbitrary rather than inherently meaningful. Assume that the dichotomization is made at the median. This means that a p49-score and p51-score are treated as opposite, and equally far from each other as scores at p1 and p99. This must inevitably be loss of information, and decrease statistical power. This is also pointed out in the literature [6], along with other drawbacks, including that dichotomization conceals possible non-linearity and reduces reliability. It should be recognized, however, that dichotomization does have one advantage, namely to yield intelligible estimates, e.g. odds ratios. However, such estimates may be presented as supplementary to those based on the original continuous variables.

### Conclusions

The authors are indeed cautionary in their conclusions, and regard their finding of an association between women's drinking and gender roles as highly tentative. This is all good, but the authors could have been more positive in their conclusions had their results been corroborated by an alternative model specification (first difference) that is more conservative than the model they used.

### References

- 1Women's gender role orientation predicts their drinking patterns: a follow-up study of Czech women. Addiction 2008; 103: 929–37.,
- 2Panel data and models of change: a comparison of first difference and conventional two-wave models. Soc Sci Res 1985; 14: 80–101., ,
- 3Causal Analysis with Panel Data (Sage University Paper Series on Quantitative Applications in the Social Sciences, 07-105). Thousand Oaks, CA: Sage; 1995.
- 4Two-wave panel analysis: comparing statistical methods for studying the effects of transitions. J Marriage Fam 2005; 67: 1061–75.
- 5Change scores as dependent variables in regression analysis. Sociol Methodol 1990; 20: 93–114.
- 6On the practice of dichotomization of quantitative variables. Psychol Methods 2002; 7: 19–40., , ,