Panel Data

Methodologic Issues for Panel Data Analysis

In cross-sectional studies, observations from study subjects are available only at a single time, whereas in longitudinal and cohort studies, individuals are assessed or observed repeatedly over time. By taking advantages of multiple assessments over time, panel data from longitudinal studies capture both betweenindividual differences and within-individual dynamics, offering the opportunity to study more complicated biological, psychological, and behavioral hypotheses than those that can be addressed using cross-sectional or time-series data. For example, if we want to test whether exposure to some chemical agent can cause a disease of interest such as cancer, the between-subject difference observed in cross-sectional data can provide evidence only for an association or correlation between the exposure and disease. The supplementary within-individual dynamics in panel data allows for inference of a causal nature for such a relationship.

Although panel data provide much richer information about the relationship among different outcomes, especially their causal nature, they raise challenging methodologic issues for study design, data analysis, and interpretation of analysis results. The two most important concerns are correlated responses and missing data. First, panel data create correlated responses because repeated assessments are collected from the same subject. For example, if we measure an individual's blood pressure twice, the two readings are correlated since they reflect the health condition of this particular individual; if he or she has high blood pressure, both readings tend to be higher than the normal range (positively correlated) despite the variations over repeated assessments. The existence of such within-subject correlations invalidates the independent sampling assumption required for most classic models, and as a result, statistical methods developed based on the independence of observations, such as the analysis of variance (ANOVA) and the multiple linear and logistic regression models, are not valid for panel data. In the blood pressure example, if we ignored the correlations between the two readings and [Page 780]modeled the mean blood pressure using ANOVA, then for a sample of n subjects, we would claim to have 2n independent observations. However, if the two readings were collected within a very short time span, say 5 σ apart, they would be almost identical and would certainly not represent independent data comparable to blood pressure readings taken from two different people. In other words, the variation between two within-subject readings would be much smaller than any two between-subject observations, invalidating the model assumption of independent observations and yielding underestimated error variance in this case. Although assessments in most real studies are not spaced as closely as in this extreme example, the within-subject correlation still exists. Ignoring such correlations by applying classic models may yield incorrect inferences.

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