Lunt Mark
ARC Epidemiology Unit, University of Manchester, Stopford Building, Oxford Road, Manchester M13 9PT, UK.
Stat Med. 2005 May 15;24(9):1357-69. doi: 10.1002/sim.2009.
There are a number of regression models which are widely used to predict ordinal outcomes. The commonly used models assume that all predictor variables have a similar effect at all levels of the outcome variable. If this is not the case, for example if some variables predict susceptibility to a disease and others predict the severity of the disease, then a more complex model is required. One possibility is the multinomial logistic regression model, which assumes that the predictor variables have different effects at all levels of the outcome variable. An alternative is to use the stereotype family of regression models. A one-dimensional stereotype model makes the assumption that the effect of each predictor is the same at all outcome levels. However, it is possible to fit stereotype models with more than one dimension, up to a maximum of min(k-1, p) where k is the number of outcome categories and p is the number of predictor variables. A stereotype model of this maximum dimension is equivalent to a multinomial logistic regression model, in that it will produce the same predicted values and log-likelihood. If there are sufficient outcome levels and/or predictor variables, there may be a number of stereotype models of differing dimension. The method is illustrated with an example of prediction of damage to joints in rheumatoid arthritis.
有许多回归模型被广泛用于预测有序结果。常用模型假定所有预测变量在结果变量的所有水平上都有相似的效应。如果情况并非如此，例如某些变量预测对疾病的易感性而其他变量预测疾病的严重程度，那么就需要一个更复杂的模型。一种可能性是多项逻辑回归模型，它假定预测变量在结果变量的所有水平上有不同的效应。另一种选择是使用回归模型的刻板印象族。一维刻板印象模型假定每个预测变量在所有结果水平上的效应相同。然而，可以拟合维度大于一的刻板印象模型，最大维度为min(k - 1, p)，其中k是结果类别数，p是预测变量数。这种最大维度的刻板印象模型等同于多项逻辑回归模型，因为它将产生相同的预测值和对数似然。如果有足够多的结果水平和/或预测变量，可能会有多个不同维度的刻板印象模型。该方法通过类风湿性关节炎关节损伤预测的例子进行说明。
