Change Over Design with First Order Residual Effects and Errors Following a First Order Autoregressive Process

Abstract

This paper deals with the problem of analysing the change over design in the presence of a first order autoregressive process for the error terms. Method of maximum likelihood has been adopted for estimating direct and first order residual effects of the treatments. A test criterion based on likelihood ratio test has been suggested for testing the autocorrelation coefficient and also the direct and first order residual effects in the presence of the autocorrelation. The conditions derived from obtaining a change over design balanced for both direct and residual effects show that a change over design balanced in the absence of autocorrelation is not necessarily balanced in the presence of autocorrelation. Patterson's (1952) series of change over designs for v=4t+3, p=½(v+1) and n=2v is an example for this.

Balanced Change‐over Designs for Autocorrelated Observations

“…We note here that the derivations of information matrices by Bora (1984Bora ( , 1985 are incorrect. In addition to other mistakes, Bora took S11 (7' in his notation) to be a diagonal matrix, whereas it is known that the off-diagonal elements of r6 involve the non-zero constants 6 and 4 (see also Kunert, 1985; G i l l & Shukla, 1987).…”

“…Kunert (1985) and G i l l & Shukla (1987) studied optimality of change-over designs for correlated observations without residual effects. Bora (1984Bora ( , 1985 tried to find suitable designs for correlated observations models, but the balancedness conditions he derived appear to be incorrect. In this paper we discuss designs for changeover experiments in the presence of additive first-order residual treatment effects and autocorrelated errors.…”

“…The standard method of analyzing data from a changeover experiment assumes independence of successive observations from an experimental subject (Williams 1949(Williams , 1950Patterson & Lucas, 1962;Hedayat & Afsarinejad, 1975), but this assumption is likely to be violated because of the temporal nature of observations. Some correlated observations models have been discussed by Finney (1956), Taka & Armitage (1983)) Bora (1984Bora ( , 1985, Kunert (1985), L a s h & Meisner (1985) and Gill & Shukla (1987). Kunert (1985) and G i l l & Shukla (1987) studied optimality of change-over designs for correlated observations without residual effects.…”

“…In particular, we observe that Williams' designs (1949Williams' designs ( , 1950 are an appropriate class when the number of periods equals the number of treatments. Bora (1984Bora ( , 1985 tried to find suitable designs for correlated observations models, but the balancedness conditions he derived appear to be incorrect.…”