Responses made on scales with ordered categories (ordinal responses) can be analysed using multinomial models which include 'threshold parameters'. These models have become established over the last 20 years, in which time research has focused on models with location terms which allow for a change in location of the threshold parameters. These location terms explain one type of difference between patterns of ordinal responses. Another type of difference can be explained by the inclusion of scaling terms in the model. Where ordinal responses are observed repeatedly on the same subject the analyst has a challenge to explain the correlation between these intra-subject responses. This thesis presents a new approach of this challenge which involves fitting one of the multinomial models, the cumulative logit model, with subject-specific location and scaling terms. These terms may be fixed effects or random effects and both cases are investigated. The approach is motivated by data from telecommunications experiments, and when used to analyse these data, it is found that the model gives a good explanation of the correlation between intra-subject responses. A new piece of general-purpose software is introduced which allows the fitting, by maximum-likelihood, of cumulative link models with both location and scaling terms. It is possible to fit the cumulative logit model by using generalized estimating equations (GEE). One particular type of GEE is discussed in detail and referred to as 'independent binomials'. An advantage to the use of this method of fitting the cumulative logit model is its straightforward implementation. Some theoretical comparisons are performed to compare the efficiency of independent-binomials estimation of model parameters with the efficiency of maximum-likelihood estimation. It is concluded that the loss of efficiency in independent-binomials cannot be considered too great to warrant its dismissal as a method of estimation.