Model the success probability of successive trials of a monkey performing a task. The 'y' variable is a vector of 0/1, with 1 denoting success on the trial; 0 failure. The fitting procedure uses logistic regression within sliding windows (specified by the 'family','binomial' arguments). Choosing the bandwidth here is critical. The data shows `on/off' behavior, exhibiting periods of mainly successes, and mainly failures, respectively. Large values of alpha will smooth out this behavior, while small values will be too sensitive to random variability. Values of 0.15 to 0.2 seem reasonable for this example. AIC is based on asymptotic approximations, and seems unreliable here -- formal model selection needs more investigation. Data is from Keith Purpura.
0001 % Model the success probability of successive trials of a monkey 0002 % performing a task. 0003 % 0004 % The 'y' variable is a vector of 0/1, with 1 denoting success on 0005 % the trial; 0 failure. The fitting procedure uses logistic 0006 % regression within sliding windows (specified by the 'family','binomial' 0007 % arguments). 0008 % 0009 % Choosing the bandwidth here is critical. The data shows `on/off' behavior, 0010 % exhibiting periods of mainly successes, and mainly failures, respectively. 0011 % Large values of alpha will smooth out this behavior, while small values 0012 % will be too sensitive to random variability. Values of 0.15 to 0.2 seem 0013 % reasonable for this example. 0014 % 0015 % AIC is based on asymptotic approximations, and seems unreliable here -- 0016 % formal model selection needs more investigation. 0017 % 0018 % Data is from Keith Purpura. 0019 0020 load 050527_correct.mat; 0021 y = byTrial(1).correct'; 0022 n = length(y); 0023 fit = locfit((1:n)',y,'family','binomial','alpha',0.15); 0024 lfplot(fit); 0025 title('Local Logistic Regression - Estimating Success Probability'); 0026 lfband(fit);