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Longitudinal data: The data arising when each of the number of subjects or patients give rise to the vector of measurements representing same variable observed at the number of different time instants.
This type of data combines elements of the multivariate data and time series data. They differ from the previous, however, in that only a single variable is involved, and from the latter in consisting of a large number of short series, one from the each subject, rather than single long series. This kind of data can be collected either prospectively, following subjects forward in time, or the retrospectively, by extracting measurements on each person from historical records. This kind of data is also often called as repeated measures data, specifically in the social and behavioural sciences, though in these disciplines such data are more likely to occur from observing individuals repeatedly under different experimental conditions rather than from a simple time sequence. Special statistical techniques are often required for the analysis of this type of data because the set of measurements on one subject tend to be intercorrelated. This correlation should be taken into account to draw the valid scientific inferences. The design of most of the studies specifies that all the subjects are to have the same number of the repeated measurements made at the equivalent time intervals. Such data is usually referred to as the balanced longitudinal data. But though the balanced data is generally the target, unbalanced longitudinal data in which subjects might have different numbers of repeated measurements made at the differing time intervals, do arise for the variety of reasons. Sometimes the data are unbalanced or incomplete by the design; an investigator might, for instance, choose in advance to take the measurements every hour on one half of the subjects and every two hours on other half.
In general, though, the major reason for the unbalanced data in a longitudinal study is occurrence of missing values in the sense that the intended measurements are not taken, are lost or are otherwise not available.
The Null Hypothesis - H0: γ 1 = γ 2 = ... = 0 i.e. there is no heteroscedasticity in the model The Alternative Hypothesis - H1: at least one of the γ i 's are not equal
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Omitted covariates is a term generally found in the connection with regression modelling, where the model has been incompletely specified by not including significant covariates.
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