multivariate ordered logit regression
res=ologit1(y,x,param,optim_func,opt_optim)
* y = (n x 1) dependent variable vector taking ncat integer values
* x = (n x m) explanatory variables matrix
* param = (k x 1) parameter vector
* optfunc = a string, the name of the optimisation function ('optim' or 'optimg')
* opt_optim = a tlist, collecting the options to the optimisation function
* res = a results tlist with
- res('meth') = 'ordered logit'
- res('y') = (nobs x ncat) matrix of data
- res('x') = (nobs x nx) matrix of data
- 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('beta') = (nvar*ncat x 1) vector of beta coefficients: [beta_1 ; beta_2 ; ... ; beta_ncat] under normalization beta_0 = 0
- res('yhat') = (nobs x ncat) matrix of fitted values probabilities: [P_0 P_1 ... P_(ncat-1)] where P_j = [P_1j ; P_2j ; ... ; P_nobsj]
- res('r2mf') = McFadden pseudo-R^2
- res('rsqr') = Estrella pseudo-R^2
- 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('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