On the Statistical Analysis of Ordinal Data When Extravariation is Present

Threshold models can be useful for analysing ordered categorical data, like ratings. Such models provide a link between the ordinal scale of measurement and a linear scale on which treatments are supposed to act. In this paper a simple agricultural plot experiment is considered with two sources of variation, namely between-plot variation and within-plot variation. It is shown that for a threshold model with two sources of variation maximum likelihood estimates can be obtained by iterative weighted least squares