XLSTAT-Conjoint uses a Newton-Raphson algorithm. It is therefore necessary to use an iterative algorithm. Unlike linear regression, an exact analytical solution does not exist. To estimate the model parameters β (the coefficients of the linear function), it seeks to maximize the likelihood function. With y being a binary variable indicating the choice of individual i for product j and J being the number of choices available to each individual. The probability that individual i chooses product j is given by:įrom this probability, we calculate a likelihood function: l(β) = Σ i=1.nΣ j=1.J y ij log(P ij) The conditional logit model is based on a model similar to that of the logistic regression except that instead of having individual characteristics, there will be characteristics of the different alternatives proposed to the individuals. The explanatory variables will also have N * 4 lines. This will also be true no matter which data transformation approach is used. Remember to re-inspect the data after transformation to confirm its suitability. In addition to log (x+1), log (2x+1) or log (x+3/8) transformation may also be used. In XLSTAT-Conjoint, you will also have to select a column associated with the name of the individuals (with 4 lines per individual in our example). Any base for the logarithm can be used, but base 10 is often used because of interpretability. The binary response variable will indicate the choice of the individual (1) and 0 if the individual did not choose this option. We have for N individuals, N * 4 rows with 4 rows for each individual associated with each transportation. As part of a conditional logit model, all four options are presented to each individual and the individual choose his preferred option. If one seeks to study transportations, for example, there will be four types of transports (car / train / plane / bike), each type of transport having its own characteristics (their price, their environmental costs.) but an individual can choose only one of four transportations. Instead of having one line per individual like in the classical logit model, there will be one row for each category of the variable of interest, per individual. The conditional logit model is a method mostly used in conjoint analysis, it is nevertheless useful when analyzing a certain type of data. (NB: the observations are not independent within a block corresponding to the same individual). The fact that the same individuals are used in taken in account by the conditional logit model. The difference is that all individuals are subjected to different situations before expressing their choice (modeled using a binary variable which is the dependent variable). The conditional logit model introduced by McFadden (1973) is based on a model similar to the logistic regression.
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