multivariate logit regression
res = multilogit1(y,x,bet0,maxit,tol)
* y = response variable vector (nobs x 1)
- the response variable should be coded sequentially from 0 to ncat, i.e., y in (0,1,2,...,ncat) entries
* x = matrix of covariates (nobs x nvar)
* bet0 = optional starting values for bet (nvar x ncat+1) (default = 0)
* maxit = optional maximum number of iterations (default = 100)
* tol = optional convergence tolerance (default = 1e-6)
* res = a results tlist with
- res('meth') = 'multilogit'
- res('beta') = (nvar x ncat) matrix of bet coefficients: [bet_1 bet_2 ... bet_ncat] under the normalization bet_0 = 0
- res('coeff') = (nvar*ncat x 1) vector of beta coefficients: [beta_1 ; beta_2 ; ... ; beta_ncat] under normalization beta_0 = 0
- res('covb') = (nvar*ncat x nvar*ncat) covariance matrix of coefficients
- res('tstat') = (nvar*ncat x 1) vector of t-statistics
- res('pvalue') = (nvar*ncat x 1) vector of corresponding p-values
- res('y') = (nobs x ncat+1) matrix of data
- res('yhat') = (nobs x ncat+1) matrix of fitted values probabilities: [P_0 P_1 ... P_ncat] where P_j = [P_1j ; P_2j ; ... ; P_nobsj]
- res('llike') = unrestricted log likelihood
- res('lratio') = LR test statistic against intercept-only model (all bets=0), distributed chi-squared with (nvar-1)*ncat degrees of freedom
- res('nobs') = number of observations
- res('nvar') = number of variables
- res('ncat') = number of categories of dependent variable (including the reference category j = 0)
- res('count') = vector of counts of each value taken by y, i.e., couunt = [#y=0 #y=1 ... #y=ncat]
- res('r2mf') = McFadden pseudo-R^2
- res('rsqr') = Estrella pseudo-R^2