Calculates overall tests based on a specified order of ante-dependence (R.W. Payne & M.S. Ridout).

Options

Treatment formula for the model at each time; if this is not set, the default is taken from the setting (which must already have been defined) of the TREATMENTSTRUCTURE directive

Block formula for the model at each time; if this is not set, the default is taken from any existing setting specified by the BLOCKSTRUCTURE directive and if neither has been set the design is assumed to be unstratified (i.e. to have a single error term)

Number of past times for which to adjust; default is maximum possible order

Limit on the number of factors in a treatment term

Parameter

Data variates (observed at successive times) for an analysis

Description

A repeated measures experiment is one in which the same set of units, or subjects, is observed at a sequence of times to investigate treatment effects over a period of time. The set of variates observed at the successive times is said to have an ante-dependence structure of order r if each ith variate (i>r), given the preceding r, is independent of all further preceding variates (Gabriel 1961, 1962). Procedure ANTTEST calculates overall tests of treatment terms based on a specified order of ante-dependence structure (see Kenward, 1987).

The data variates are supplied, as a list, by the DATA parameter. The variates may contain missing values, provided these are "dropouts", that is, once a unit becomes missing it should remain missing at all subsequent times.

The model for the design is specified by options of the procedure. TREATMENTSTRUCTURE specifies a model formula to define the treatment terms in the analysis; if this is unset, ANTTEST will use the model already defined by the TREATMENTSTRUCTURE directive, or will fail if that too has not been set. BLOCKSTRUCTURE defines the underlying structure of the design, and ANTTEST will use the model (if any) previously defined by the BLOCKSTRUCTURE directive if this is not set; these can both be omitted if there is only one error term (i.e. if the design is unstratified). Option ORDER specifies the order of ante-dependence structure to be assumed for the tests; by default, this is taken as the maximum possible order (the smaller of the number of times minus one or the number of residual degrees at each time). A suitable order can be established using the ANTORDER procedure. The FACTORIAL option can be used to set a limit on the number of factors in the terms generated from the treatment formula.

Method

The procedure uses the method of Kenward (1987) to calculate the statistics using residual sums of squares from analysis of covariance. For further details of ante-dependence see Gabriel (1961, 1962).

Action with RESTRICT

References

Gabriel, K.R. (1961). The model of ante-dependence for data of biological growth. Bulletin Institut International Statistique (Paris), 39, 253-264, (33rd session).

Gabriel, K.R. (1962). Ante-dependence analysis of an ordered set of variables. Annals of Mathematical Statistics, 33, 201-212.