# mclogit: Mixed conditional logit models in R

The package ‘mclogit’ implements the estimation of *mixed conditional logit* models via the PQL method as used in my article published in *Electoral Studies*. It is published on CRAN. Development occurs on GitHub, where both releases and the development tree can be found.

The probability that individual \(i\) chooses alternative \(j\) from choice set \(\mathcal{S}_i\) is \[ \pi_{ij} = \frac{\exp(\eta_{ij})}{\sum_{k\in\mathcal{S}_i}\exp(\eta_{ik})} \] with \[ \eta_{ij}=\beta_1x_{1ij}+\cdots+\beta_qx_{qij}+U_{ij} \] where \(x_{hij}\) are values of independent variables, \(\beta_h\) are parameters (coefficients), and \(U_{ij}\) are random effects with a normal distribution.

The package allows to specify that random effects are equal for all individuals within clusters \(\mathcal{C}_c\), that is \(U_{i_1j}=U_{i_2j}\) for \(i_1\in\mathcal{C}_c\) and \(i_2\in\mathcal{C}_c\), where such clusters also may be nested in a “multi-level” manner.

The “dependent variable” \(y_{ij}\) may be a “dummy variable” that is equal to 1 if individual \(i\) has chosen alternative \(j\) and 0 if s/he has chosen another alternative. For example, if all individuals \(i\) face the same set of five alternatives, then five values of the dependent variable would correspond to each individual with only one of the values being equal to one and the other four values being equal to zero. (This is sometimes called that the data are in “stacked” format.)

Also, if “covariate classes” of individuals are formed that share the same values of the independent variables *and* are members of the same cluster, and \(i\) indicates such a covariate class, \(y_{ij}\) may be the count of individuals from covariate class \(i\) that have chosen alternative \(j\).