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I have the variables $Y$, $x_{m1}$, $x_{m2}$, $\ldots$, $x_{mn}$, $x_{p1}$, $x_{p2}$, $\ldots$, $x_{pn}$, $x_{q1}$, $x_{q2}$, $\ldots$, $x_{qn}$.

$Y$ is the class label (0 or 1). $x_{mj}$, $x_{pj}$ and $x_{qj}$ can be regarded as the same kind of property, but different combination of three properties can predict different $Y$. Actually, $x_{m1}$, $x_{m2}$, $\ldots$, $x_{mn}$, $x_{p1}$, $x_{p2}$, $\ldots$, $x_{pn}$ and $x_{q1}$, $x_{q2}$, $\ldots$, $x_{qn}$ came from three subclasses. The subclasses' label determine the final $Y$. I have such kind of a dataset, I want to do inference with logistic regression and then use the new model to predict new $y$ given $x$.

The simplest method is to deem every $x$ as independent and do the logistic regression, I don' think this method is effective, using interaction may be another choice. Can anyone tell me how to solve this problem or have some other suggestions by using other models.

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    $\begingroup$ what is 'weird' about it? $\endgroup$ – Peter Ellis Apr 13 '13 at 3:08
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    $\begingroup$ also can I clarify what you mean by "the subclasses' label determine the final Y". I presume you do not mean literally "determine", but that there is some unexplained or random element of Y? $\endgroup$ – Peter Ellis Apr 13 '13 at 3:11
  • $\begingroup$ final comment from me - why don't you think using every x as an explanatory variable will be effective as a modelling strategy (I'm not saying it will be, just wondering why you have ruled this out - I can think of several possible reasons). $\endgroup$ – Peter Ellis Apr 13 '13 at 3:13
  • $\begingroup$ Peter, thanks for your comment. I may not illustrate my question well. Here, I use an example. Suppose the combination of xm1, xm2, …, xmn can determine ym as 0 or 1, the combination of xp1, xp2, …, xpn, xq1 can determine yp as 0 or 1 and combination of xq1, xq2, …, xqn can determine yq as 0 or 1. When ym=0, yp=1, yq=0, then the final Y is 1, all of the other combination of ym, yp and yq can make Y as 0. $\endgroup$ – user22062 Apr 13 '13 at 3:46
  • $\begingroup$ I think I can not deem every x as independent, so if I directly use logistic regression, I think the result may be not good. I am not sure if I need to add the interaction. $\endgroup$ – user22062 Apr 13 '13 at 3:51

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