To model the relationship between winning the Oscars (Y) and predictors (denoted, X), we sought to use a penalised conditional logistic regression model. Suppose we have K independent competitions, each comprising of nominees, the conditional likelihood per stratum ( k ) can be written as
where is the set of collection of
sets
where
. Consequently we can write the likelihood as
In high-dimensional settings, penalized methods such as the Lasso could potentially reduce variance (to improve prediction accuracy) and to identify the subset of predictors that exhibit the strongest link with the response. We therefore recast our likelihood to include the penalisation.
Our problem is now expressed as
where the parameter is estimated using cross-validation. The model allows us to bound the coefficient such that
for a pre-specified parameter t . To model the probability of winning the oscar price, we first standardize our predictors.
Lamin Juwara
## optimal lambda value:
## [1] 2.132296
Next, we present the values of corresponding to the best value of
.
## estimated betas:
## All Predictions for 2020 Oscars:
## Winners for 2020 Oscars:
The predicted winners are
