# Is the weights= option in lmer() doing what I want?

I want to predict PGA golfer performance. I'm wondering if I am correctly giving more weight to more recent results by using the weights= option in the lmer() function.

I have data from 2012-2014 laid out thusly:

library("lme4")
library("dplyr")

Source: local data frame [6 x 5]
Groups: plrF, trnF

plrF trnF rdF wt rdScr rdPar
1    5  996  R1  1    71    71
2    5  996  R2  1    69    71
3    5  996  R3  1    70    71
4    5  996  R4  1    69    71
5    5  998  R1  3    72    72
6    5  999  R1  4    73    70

• plrF - Player ID
• trnF - trounament ID
• rdF - round of tournament (each tournament has 4 rounds)
• wt - Weight. Basically number of weeks since Jan 1, 2012.
• rdScr - observed score for a golfer
• rdPar - par for that round.

I want to use lmer() to model player scores based on a random player effect, and fixed par effect. Let's split the data into a training set and testing set.

oRdDat <- rdDat %>% filter(wt <= 120)
newdat <- rdDat %>% filter(wt > 120)


Fit a model on the observed data:

lmr1 <- lmer(rdScr ~ rdPar + (1 | plrF), data= oRdDat)


Use the results to predict the new data, and calculate the absolute error of our prediction:

pred0 <- cbind(newdat, prScr = predict(lmr1, newdat, allow.new.levels = TRUE)) %>%
mutate(diff = abs(prScr - rdScr))


and use that diff variable to check the Mean Absolute Error of our projection:

summary(pred0$diff) Mean 2.481  However, I think it is very reasonable to assume more recent results (eg late 2014) should have more of an impact on our projection than results from early 2012. So I fit this: wlmr1 <- lmer(rdScr ~ rdPar + (1 | plrF), weights = wt, data= oRdDat)  Predict as before and check out the MAE: summary(pred1$diff)
Mean
2.474


Incremental improvement! :-D

Let's leave aside the question of what the optimal weighting scheme would be and whether the small improvement seen here is actually 'worth it'. My question is: Is that weights=wt option doing what I want it to do? Eg, provide more weight to more recent results in terms of projecting future scores?

Thanks!

The log-likelihood is defined as: $$\log(L(\boldsymbol{\theta})) = \sum_{i = 1}^{n} w_i \log(P(y_i | \boldsymbol{x}_i, \boldsymbol{\theta}))$$ where $\boldsymbol{\theta}$ are the model parameters, $w_i$ is the weight for observation $i$, $y_i$ is the response for observation $i$, and $\boldsymbol{x}_i$ is the vector of covariates for observation $i$. So, yes, I think the weights option is doing exactly what you want - the more recent observations have a greater contribution to the log-likelihood.