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I am attempting to use Dixon & Coles (1997) method of predicting soccer matches but rather than estimate a model predicting both team's goals scored (bivariate poisson) I'm simply predicting the game outcome (home team win, lose, or draw) using an ordered probit. The authors estimate a dynamic model where games in the past are down-weighted by a negative exponential function so that the psuedo-likliehood function in my research should be
which presumably can be estimated via maximum likelihood.
My question is, can I use iweights to accomplish this in Stata? My code is
Code:
oprobit y x [iw=xi]
Does this estimate the equation above as written and what, if anything, does iweights do to the estimated variance-covariance matrix?
According to the Methods and Formulas section from ologit (where readers are redirected for oprobit), optional weights enter the log-likelihood function as
\[ \ln L = \sum_{j=1}^Nw_{j}\sum_{i=1}^{k}I_i(y_j)\ln p_{ij} \] where \[ln p_{ij}\] is the natural log of the probability that observation i has outcome j, \[w_{j}\] are the optional weights so my guess is it is working as planned but I'm not 100% sure and there's no mention of what iweights do to the variance-covariance matrix.
I am attempting to use Dixon & Coles (1997) method of predicting soccer matches but rather than estimate a model predicting both team's goals scored (bivariate poisson) I'm simply predicting the game outcome (home team win, lose, or draw) using an ordered probit. The authors estimate a dynamic model where games in the past are down-weighted by a negative exponential function so that the psuedo-likliehood function in my research should be
which presumably can be estimated via maximum likelihood.
My question is, can I use iweights to accomplish this in Stata? My code is
Code:
oprobit y $x [iw=xi]
where $x is the global for all game-level variables and xi is the variable I made to represent
\[exp(-\xi (t-t_j)) \]
for each game. Does this estimate the equation above as written and what, if anything, does the use of iweights do to the estimated variance-covariance matrix?
According to the Methods and Formulas section from ologit (where readers are redirected for oprobit), optional weights enter the log-likelihood function as
\[ \ln L = \sum_{j=1}^Nw_{j}\sum_{i=1}^{k}I_i(y_j)\ln p_{ij} \]
so my guess is it is working as planned but I'm not 100% sure and there's no mention of what iweights do to the variance-covariance matrix.
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