Longitudinal Vs. Cross-sectional Analysis

Dr. D. R. WeerasekeraDepartment of Statistics, University of Colombo

The survey literature distinguishes cross-sectional and longitudinal designs, butmost surveys conducted in practice are based on cross-sectional designs. Thelimitations of these cross sectional surveys are that they are confined to a specificpoint in time. That is, they provide us with a snapshot of a sample of a populationat a single point in time. Since population characteristics constantly change overtime, cross-sectional surveys for such situations do not reflect the actual situation.This raises the issue of measuring social characteristics over time in a single study –the objective of a longitudinal study. The study of change over time is calledlongitudinal analysis. In this sense, longitudinal studies involve the study of aprocess of change over a period of time. Such trends can also be observed bycomparing the results of surveys that are conducted in separate years. The aim ofthis paper is to point out the importance of conducting longitudinal surveys for avariety of situations, and the importance of applying the correct statisticaltechniques for data obtained from longitudinal surveys.

The simplest type of longitudinal analysis of survey data is called trend analysis,which examines overall change over time. Trend analysis has some significantlimitations. While it can reveal changes, it gives us little insight as to how or whythe changes have taken place. One possibility is that individuals change theirattitudes or behaviors as they move through the life cycle. Another possibility isthat people change because of new circumstances. A major crisis, such as a war ordepression may result in such changes across all age groups. Changes in technologymay have a similar impact.

Cross-sectional surveys often provide data that reveal little change from one yearto the next. This can be seen especially, when we consider figures onunemployment or characteristics of poor households receiving Samurdhi-benefits –implying that the same households remain poor over time. On the other hand,several longitudinal studies point to considerable variation over time among poorhouseholds and reveal that they are in a transition state. Thus, some householdstypically move between states of poverty; others move from a state of poverty torelative affluence; others slide into states of poverty. Longitudinal surveys furtherenable us to detect and monitor variations and trends among individuals, as in thecase of variations in salary among workers. Here the value of collecting data atseveral points in time cannot be measured as changes in the job patterns andincomes of people can be monitored effectively only at an individual level.

Repeat surveys, on the other hand, offer a distinct advantage as they enable us tocapture the net effect changes. In the case of an opinion poll, such net effectsmight be expressed as overall increase or decrease in the number of people whoreport an intension to vote for a specific party. By repeating the survey at adifferent time and asking fairly similar questions, it enables us to collectinformation that can easily be compared. However, repeat surveys collect datafrom different respondents and thus we are unable to determine the gross changesin the intention to vote. This limitation is clear from the inability of cross-sectionaland repeat surveys on voting patterns to provide detailed information aboutrespondents who are undecided about whether they vote in an election.

One example of a cohort study in a country is that a birth cohort is being followedover a ten-year period in order to monitor changes in their lives. In such a survey,the same respondents are interviewed at different times during the study. Here, (a)data are collected at two or more different points in time; (b) the same sample isinterviewed at distinct points in time; and (c) data from the respondents arecompared across these time points in order to monitor patterns of change andpromote social understanding.

In panel studies, the same people are interviewed at two or more points in time.Since the sample is the same, any changes we observe are not a result of samplingerror. Panel studies, however, have problems of their own. For one thing, they aregenerally very expensive, as it is not easy to keep track of respondents. Further,despite our best efforts, we may not be successful in all of our attempts to re-contact respondents, especially if the study is conducted over a long period of time.Those who drop out of the panel (by moving, dying, refusing to continue, etc.)may have changed their attitudes and behaviors from those who remain.

The main disadvantages of longitudinal surveys are that they are costly.

In longitudinal studies, individuals are measured repeatedly through time or thesame variable is measured repeatedly. Therefore, longitudinal data requiresophisticated statistical techniques because the repeated observations are usually(positively) correlated. Correlation must be accounted for to obtain validinferences. Sequential nature of the measures implies that certain types ofcorrelation structures are likely to arise. One approach to analyzing repeatedmeasures data is to consider extensions of the one-way ANOVA model thataccount for the covariance. That is, rather than assuming that repeatedobservations of the same subject are independent, it allows the repeatedmeasurements to have an unknown covariance structure. To do this, we can easilyuse the SAS procedure, PROC MIXED, an extension of PROC GLM which allowsclusters of correlated observations.