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Predicting Survivor 7: Predictions from an Empirical Modelby Jeffrey D. Sadow -- 09/15/2003
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Inquiring minds want to know why the predictive models I used last time for Survivor 6 (based on editions 1-5) performed so abysmally, and whether accurate predictions can and will be made for Survivor 7. (Readers should click on the link above if they want all the details of the models’ derivations and explanation of basic terms and concepts in some methods of statistical analysis.)
After a lot of cogitation and number-crunching, the answer to the first question is … I don’t know. Just looking at the discriminant analysis, most of the damage occurred outside the middle (jury members not in the finals), predicting finalists off the jury and vice-versa. There were more misclassifications for this installment than any other, and of these misclassifications, they were more often off by two categories than by one than in any other installment.
Different factors seemed to be at work in the most recent series. Recall that the important factors for both discriminant and ordinary least-squares regression (OLS) models for the first five were appearance in the website photo (contestants considered more likely to win were those who had bigger smiles, who wore less drab and covering clothing, and who did not wear jewelry), family structure (those married and especially so with children were thought to do better), and gender (men, other things equal, had an advantage). But for the sixth installment, while appearance again was particularly significant, family and sex was not and race and occupational category were (whites were favored as were higher-status individuals).
The original OLS model originally used produced some mind-boggling errors, as many as 11 places in some instances, in all of the bottom, middle, and top equally. The revised model using the three independent variables found significant for this series did a much better job. But hindsight is 20/20.
Reanalyzing by OLS the entire 96 contestants (by analyzing all predictors, then tossing the least significant until only significant ones were left), while appearance obviously continues to be by far the most powerful predictor, and sex stays in there as well, family was replaced by race. The equation looks like this:
Predicted finish place = 12.692 – 1.344 x appearance + 1.829 x sex + 1.353 x race
Thus, the maximum score of a white male who smiled big and wore open, colorful clothing without jewelry would be a prediction to finish in 5.122th place, and the minimum score of an Asian female who didn’t smile, wore much dab clothing and jewelry would be predicted to finish 17.837th (notice the boundary problem with the end points of the model, which should be close to 1 and 16 – there because the explained variance is a paltry 13.4%, meaning the model doesn’t tell us much).
Another interesting point – if including skill level - that is, the combination of leadership roles held in the past, interactivity of past jobs, and educational attainment - and also shareability of luxury item, this creates a better-predicting equation, even if skill level is, by the 10% probability level I use to denote significance, not significant in this equation set of five independent variables. But I don’t include this since there’s not theoretical reason to assume these should be control, rather than independent, variables. If these last two sentences totally bored you, relax; only those really interested in statistics would care to understand the implications.
Which are, this model may be too unstable for my liking. So I tried again, this time disaggregating the appearance and skill variables. This time, I got a better model, even if it explains a still-paltry, but higher, 18.6 percent of the variance:
Pred.fin. = 12.645 + 1.733 x race + 0.351 x status – 1.879 x clothes – 2.487 x jewelry
Both race and status have become significant. With another white winner of the game and minorities finishing far down the line this time, perhaps this has pushed this factor into prominence. Status, as measured by a rough indicator of occupation, theoretically should demonstrate that success in the economic world may draw upon the same qualities that bring success in Survivor.
Meaning a white professional with loose, undrab clothes and not wearing jewelry could expect 4.118th place, while an Asian menial employee with drab, covering clothes and jewelry would get 18.37th place. Still a bit of a boundary problem, but marginally it’s better. And its best results come with only significant variables included (other indicators such as the standard error of the estimate and F-score looked better – again, don’t mind this stuff unless you are into statistical analysis). Therefore, I chose these variables for this crack at predicting.
So, let’s see how OLS predicts Survivor 7 here and what some discriminant analysis comes up with. (Unfortunately, the database is down one variable for this one because CBS no longer gives contestants’ luxury items information on its website.) Again, given the model’s low explanatory power (as well as for theoretical reasons), OLS results will be used to fine-tune the result garnered from discriminant analysis.
The Survivor 6 results produced some interesting changes in the discriminant model, for I used a stepwise strategy in determining suitable variables (for the record, entrance at p=.09, removal at p=.10) which came up with the same two clothing and jewelry variables, but also age rather than status. The last is interesting for some correspondents with me have suggested the fact that in Survivor 6 the fact it featured the youngest average-aged cast ever plus their distribution within the two tribes (originally and when swapped) was what swamped my model. Perhaps this is some empirical verification of what was noted on the surface.
It’s difficult to tell in terms of direction (that is, whether being younger or older is advantageous) how age empirically affects prediction in discriminant analysis since absolute distances are sought to be minimized. Surface evidence from Survivor 6 may suggest the younger have the bonus; perhaps youth and vigor beats guile - especially when it comes to physical challenges, but also mental because it’s harder to think straight the more depleted you are.
Now with four variables that could produce three planes on which to locate predicted scores, I decided to create quartiles of categories to take advantage of the additional information I could get with the increased number of planes (more is always better when it comes to prediction. As readers from the Survivor 6 predictive attempt recall, this way we get more accurate measures of correct classification of predicted vs. actual finishes. In fact, this effort produced a healthy 46.9% percent correct classification rate over the first six series, nearly double that of chance with four categories (25%).
It is this model that I will employ. Predicted placements below are listed by the quartile predicted by the discriminant analysis (which overweighed into the first and third and underweighed into the second and fourth quartiles), then by placement predicted by OLS, then how well the two matched (where a positive score meant discriminant picked a lower quartile than did OLS), and finally a revised placement that first ordered contestants by quartiles, then within quartiles:
As can be seen, in half the cases discriminant analysis agreed with OLS regression. In six of the misses, they were fairly borderline. In the cases of Burton and Andrew, OLS predicted second quartile finishes while discriminant has them as early ejectees. In fact, visually plotted Burton nearly slipped into the second quartile and Andrew nearly into the first. So Andrew’s placement may be the most imprecise of all. But there is remarkable unity on the finalists – Shawn, Jon, Lillian, and Trish, with Shawn picked to win it all.
So those are my picks and I’m sticking with them. Maybe this time some weird dynamics won’t present themselves and ruin several hours of number-crunching.
Jeffrey D. Sadow is an associate professor of political science at Louisiana State University in Shreveport where he teaches, among other things, classes in international politics, international organizations, and diplomatic history. He has published in the area of gaming simulations in international politics.
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