OptiPt                  package:eba                  R Documentation

_E_l_i_m_i_n_a_t_i_o_n-_B_y-_A_s_p_e_c_t_s (_E_B_A) _M_o_d_e_l_s

_D_e_s_c_r_i_p_t_i_o_n:

     Fits a probabilistic choice model by maximum likelihood
     estimation.

_U_s_a_g_e:

       OptiPt(M, A = 1:I, s = rep(1/J, J))

       summary.eba(object, ...)

_A_r_g_u_m_e_n_t_s:

       M: a square matrix or a data frame consisting of absolute
          frequencies

       A: a list of vectors consisting of the stimulus aspects; the
          default is '1:I', where 'I' is the number of stimuli

       s: the starting vector with default '1/J' for all parameters,
          where 'J' is the number of parameters

  object: an object of class 'eba', typically the result of a call to
          'OptiPt'

     ...: additional arguments affecting the summary produced

_D_e_t_a_i_l_s:

     The probabilistic choice models which can be fitted to
     paired-comparison data are the Bradley-Terry-Luce (BTL) model,
     preference tree (Pretree) models, and elimination-by-aspects (EBA)
     models, the former being special cases of the latter.

     'A' is usually a list of vectors, the first element of each being
     a number from 1 to 'I'; additional elements specify the aspects
     shared by several stimuli. When fitting a BTL model, 'A' reduces
     to '1:I', i.e. there is only one aspect per stimulus.

     The maximum likelihood estimation of the parameter values is
     carried out by 'nlm'.  The Hessian matrix, however, is
     approximated by 'fdHess{nlme}'.  The likelihood function 'L' is
     called automatically.

_V_a_l_u_e:

estimate: a vector of parameter estimates

      se: a vector of the standard errors of the parameter estimates

    ci95: the 95%-confidence intervals for the parameter estimates

logL.eba: the log-likelihood of the fitted model

logL.sat: the log-likelihood of the saturated (binomial) model

goodness.of.fit: the goodness of fit statistic including the likelihood
          ratio (-2logL), the degrees of freedom, and the p-value of
          the corresponding chi2 distribution

 u.scale: the u-scale of the stimuli; one scale value is defined as the
          sum of aspect values (parameters) that characterize a given
          stimulus

 hessian: the Hessian matrix of the likelihood function

   cov.p: the covariance matrix of the model parameters

 chi.alt: the Pearson chi2 goodness of fit statistic

  fitted: the fitted paired-comparison matrix

      y1: the data vector of the upper triangle matrix

      y0: the data vector of the lower triangle matrix

       n: the number of observations per pair ('y1 + y0')

      mu: the predicted choice probabilities for the upper triangle

_A_u_t_h_o_r(_s):

     Florian Wickelmaier

_R_e_f_e_r_e_n_c_e_s:

     Wickelmaier, F., & Schmid, C. (2004). A Matlab function to
     estimate choice model parameters from paired-comparison data.
     _Behavior Research Methods, Instruments, and Computers_, *36*,
     29-40.

     Bradley, R.A. (1984). Paired comparisons: some basic procedures
     and examples. In P.R. Krishnaiah & P.K. Sen (eds.), _Handbook of
     Statistics, Volume 4_. Amsterdam: Elsevier.

     Tversky, A. (1972). Elimination by aspects: A theory of choice.
     _Psychological Review_, *79*, 281-299.

     Tversky, A., & Sattath, S. (1979). Preference trees.
     _Psychological Review_, *86*, 542-573.

_S_e_e _A_l_s_o:

     'strans', 'cov.u', 'wald.test', 'group.test', 'plot.eba',
     'residuals.eba', 'nlm'.

_E_x_a_m_p_l_e_s:

     data(celebrities)  # absolute choice frequencies
     A <- list(c(1,10), c(2,10), c(3,10), c(4,11), c(5,11), c(6,11),
               c(7,12), c(8,12), c(9,12))  # the structure of aspects
     eba <- OptiPt(celebrities, A)  # Fit a preference tree

     summary(eba)  # goodness of fit
     plot(eba)  # residuals versus predicted values

     ci <- 1.96 * sqrt(diag(cov.u(eba)))  # 95%-ci of the preference scale
     a <- barplot(eba$u, ylim = c(0, .35))  # plot the scale
     arrows(a, eba$u-ci, a, eba$u+ci, .05, 90, 3)  # error bars

