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Most competing hazards models are based on the rather strong assumption that alternative destinations are stochastically independent. Individual- specific unmeasured risk factors that are shared by two or more alternatives are, as a result, ruled out. The present paper develops a generalization of the standard discrete-time competing hazards model that allows for the types of stochastic dependencies resulting from shared unmeasured risk factors. An empirical example is provided using the process by which young women form their first conjugal residential union, with married and unmarried cohabitation representing the competing alternatives. The results suggest considerable and significant similarity of the alternatives in terms of the unmeasurables. It is also shown that, as a result, the independence assumption leads to substantially biased estimates of the net marriage and net cohabitation survival functions. While the model does require a temporal independence assumption, Monte Carlo simulations indicate that the biases introduced by violations of this assumption are confined primarily to the estimates for time-varying covariates. Estimates for other covariates and the cross-destination correlation coefficient, itself, are relatively robust.