In longitudinal research one or more samples of n subjects are observed t times on d variables. Each variable may either be constant or change across time. Parameters that systematically vary display a trend (cf. Anderson 1971; Metzler and Nickel 1986). For instance, time series have a trend in location if the mean of the observed variable systematically varies over the t observation points. Examples of trends in location include monotone linear trends, that is, constant increases or decreases in the mean. Other time series may have a quadratic trend, that is, they look either U-shaped or inversely U-shaped. Still other time series may have a trend in dispersion. For instance, it has been hypothesized that the dispersion of intelligence increases during childhood and adolescence and decreases during senescence.

If we analyze ordinal or continuous variables, we are interested chiefly in trends in location. If we analyze nominal variables, on the other hand, we are interested in shifts from one configuration to another. Trends in location at the ordinal level can be identified by cases that, t later points in time, show higher or lower scores than those observed at earlier points in time. For example, suppose a psychotherapist uses a seven point scale to measure patient anxiety, with higher scores indicating more anxiety. An example of a trend would be a monotonous decrease in scores on the scale, across time.