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An alternative method for longitudinal binary or multivariate binary data is the

latent Markov model, an extension of the standard Markov model, where the states are unobserved. An important assumption is that the disease or other process can be represented as a series of states, e.g., stages of a disease as for cancer or presence and absence of disease. This is in contrast to the latent trajectory model where a subject remains in the same class, defined only by level of symptoms at each time point and avoiding assumptions about disease states. For classifiying subjects, the mixed latentMarkov model (Langeheine and van de Pol, 1990, 1993), which models the population as a mixture of latentMarkov models, can be used, but still requiring the assumptions of disease states. The latent trajectory model is closer to the random

effects and marginal models that are commonly used in many areas of statistics, requiring fewer assumptions and having the advantage of being able to incorporate heterogeneity within classes, which is appropriate for the data set analysed here.

Ware and Lipsitz (1988) showed that results from the two methodologies may be similar in some cases for repeated categorical data, and Follmann (1994) describes the need for both for analysing repeated categorical data. Estimation for the latent Markov models may also be more difficult as size of the transition matrices increases rapidly as the number of underlying classes increases.

Several authors have fittedmodels for a single binary longitudinal outcome, applying standard latent class techniques, e.g., Fink et al. (1993) andCroudace et al. (2003). Vermunt and van Dijk (2001) analysed longitudinal data with multiple binary outcomes at each time point by summarizing the data.

The data on attitudes to abortion over time consisted of the responses to a series of situations where a woman might require an abortion and the respondent would register approval or disapproval of each situation.

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In their analysis, the detail of the responses was ignored, and subjects’

attitudes were summarized by the total number of approvals at each time point.

Latent class models assume homogenous classes.

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This assumption is unlikely to be correct as in most cases a class will correspond to a range of outcome probabilities.This heterogeneity may result from different levels within a class, e.g., severity of disease or degree of attitude.

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縱向二進制或多維分佈的二进制数据的一個交替法是潛在馬爾可夫模型，標準馬爾可夫模型的引伸，狀態是未受注意的。 一個重要假定是疾病或其他過程可以代表作為一系列的狀態，即，一種疾病的階段至于癌症的或出现和缺乏疾病。 這是與主題在同班依然是的潛在彈道模型對比，僅定義由症狀的水平在每次指向和避免關於疾病狀態的假定。 為classifiying的主題，可以使用混雜的latentMarkov模型(Langeheine和van de Pol， 1990年， 1993)，塑造人口作為latentMarkov模型混合物，但是仍然要求疾病狀態的做法。 潛在彈道模型是離任意較近是常用的在統計許多区域，要求少量假定和有好處的能合併在類之內的非均勻性，為被分析的数据集是適當的這裡的作用和少量的模型。 ware和Lipsitz (1988)表示，從二方法學的結果也許在某些情況下是相似的為重複的绝對數據和Follmann (1994)描述對兩個的需要分析的重複的绝對數據。 潛在馬爾可夫模型的估計也許也是更加困難的，當跃迁矩阵的大小迅速地增加，當部下的類的数量增加。即，幾位作者有一個唯一二進制縱向結果的fittedmodels，等申請標準潛在類技術等Fink (1993) andCroudace (2003)。 Vermunt和範戴克(2001)分析了與多個二進制結果的縱向數據在每次通过總結數據指向。