Assesses order of ante-dependence for repeated measures data (M.S. Ridout & R.W. Payne).

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)

Maximum order against which to test; 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 ANTORDER calculates statistics to assist in the selection of an appropriate order of ante-dependence structure for sets of repeated measures data, using the method of Kenward (1987). Once the order of ante-dependence structure has been established, the individual variates can be analysed individually by analysis of covariance, adjusting for the r previous variates, to assess the times at which treatment effects occurred. Also, procedure ANTTEST can be used to perform overall tests of treatment effects.

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, ANTORDER 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 ANTORDER 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 MAXORDER specifies the maximum order of ante-dependence structure to be tested; 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; see Kenward 1987). 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.