#_____________________________________________________________________________________________ # R code accompanying Verkuilen, Smithson, Kievit, Zand Scholten #_____________________________________________________________________________________________ # This simulation illustrates the assignment of membership values to a fuzzy set in the # context of diagnosis of Major Depressive Disorder (MDD). # First, np persons with different probabilities of displaying ns symptoms are simulated. # Second, these probabilities are transformed to 'observed' scores indicating whether a # symptom is actually displayed or not. # Third, membership to the set of clinically depressed persons (displaying MDD) is assigned. # Assigment is performed using different methods: # 1) DSM procedure: person is classified as depressed when displaying 5 or more symptoms # 2) Direct Assignment: person is assigned value by summing weighted symptom scores # 3) Assignment using indirect scaling of symptoms (iss): This is the weighting summation of the 9 symptoms. #_____________________________________________________________________________________________ # SIMULATION OF PERSONS, SYMPTOMS, SYMPTOM PROBABILITIES AND SYMPTOM SCORES np = 10000; # Number of simulated persons ns = 9; # Number of symptoms a = rep(1,ns); # Discrimination parameters used to generate symptom probabilities b = c(-1.80,-0.58,-0.37, -0.21,-0.21,-0.18, 0.90, 0.95,2.47);# Difficulty parameters used to generate symptom probabilities (see Aggen et al.) t = rchisq(np,2); # Chisquare distributed latent values t = ((6*t)/max(t)-3); # Rescaling to range [-3,3] prob = matrix(,np,ns); # Matrix will contain probabilities of displaying each of ns symptoms for np persons # Generates probability of displaying a certain symptom according to 2pl IRT model for each of np persons for(s in 1:ns) { # For each symptom s prob[,s]=exp(a[s]*(t-b[s]))/(1+exp(a[s]*(t-b[s]))); } score = matrix(,np,ns) # Matrix will contain dichotomized scores, indicating whether symptom is displayed (1) or not (0) # Generates dichotomous score by sampling from a binomial distribution for each of np persons with probability determined earlier for(s in 1:ns) { # For each symptom s score[,s]=rbinom(np,1,prob[,s]); } # Symptom names colnames(score)=c("Depressed", "Weightapp", "Nointerest", "Sleepprob", "Fatigue", "Psycmotor", "Worthless", "Concentra", "Suicidal"); # All data aggregated in a data frame data = data.frame(cbind('Theta'=t, score)); #_____________________________________________________________________________________________ # DIFFERENT ASSIGMENT METHODS #1 Assigment using DSM criteria (dsm). Assuming these symptoms are all longer than two weeks, >5=depressed sms = rowSums(score); # summing into a symptom count for each person dsm = ifelse(sms>5,1,0); # recoding into 1 if symptom count > 5, else 0 #2 Direct assignment (das): Symptoms are weighted by using linear regression weights obtained from a sample of persons who # are assigned membership values directly by experts. Here we use the original latent scores as direct assignment values data = data.frame(cbind('Theta'=t, score, sms, dsm, iss)); # All data aggregated in a data frame # beta weights obtained from linear regression of theta on ns symptom scores bts = lm(Theta ~ Depressed + Weightapp + Nointerest + Sleepprob + Fatigue + Psycmotor + Worthless + Concentra + Suicidal, data)\$co; bwts = matrix(rep(bts[-1],np),np,ns,T); # Matrix of beta weights repeated np times bwsc = bwts*score; # Symptom scores for np persons multiplied by beta-weights das = rowSums(bwsc); # The weighted sum score das = das/sum(bts[-1]); # Dividing weighted sumscore by max score, rescaling to range[0,1] data = data.frame(cbind(data,das)); # Adding das score to data layout(matrix(1:2,1,2)); hist(t) hist(rowSums(score)) #3 Assignment using indirect scaling of symptoms (iss): This is the weighting summation of the 9 symptoms. #weights = matrix(rep(c(.03,.04,.07,.09,.11,.12,.13,.17,.24),np),np,ns,T); # Symptoms weights that sum to 1. These are example weights and may be adapted weights = matrix(rep((b+1.8)/sum(b+1.8),np),np,ns,T); # Weights based on Aggen et al. wscore = weights*score; # multiplying weights by presence of symptom for each person to get weigted score iss = rowSums(wscore); # the weighted sum score