# Calculate latent traits for a given response matrix and item parameters using MLE This function calculates the MLE of latent traits for a given response matrix with rows being examinees and columns being items for given item parameters. ```r computeAbility(respMat, dscrmn = dscrmn, dffclt = dffclt, c = rep(0, length(dffclt)), parallel=FALSE) ``` ## Arguments - `respMat`: The response matrix of 0 and 1 with rows being examinees and columns being items. - `dscrmn`: A vector of item discrimination parameter. - `dffclt`: A vector of item difficulty parameter. - `c`: A vector of guessing parameter. Default is set to all 0 indicating no guessing allowed. - `parallel`: Logical indicating whether to use parallel computing with foreach package as backend. ## Details This function is a wrapper of the thetaEst() function from catR package (Magis, 2012). ## Returns A vector of latent trait estimates for each examinee. ## References David Magis, Gilles Raiche (2012). Random Generation of Response Patterns under Computerized Adaptive Testing with the R Package catR. Journal of Statistical Software, 48(8), 1-31. ## Author(s) Pan Tong (nickytong@gmail.com), Kevin R Coombes (krc@silicovore.com) ## See Also `fitOnSinglePlat, intIRTeasyRun, calculatePermutedScoreByGeneSampling` ## Examples ```r # number of items and number of genes nSample <- 10 nGene <- 2000 set.seed(1000) a <- rgamma(nSample, shape=1, scale=1) b <- rgamma(nSample, shape=1, scale=1) # true latent traits theta <- rnorm(nGene, mean=0) # probability of correct response (P_ij) for gene i in sample j P <- matrix(NA, nrow=nGene, ncol=nSample) for(i in 1:nSample){ P[, i] <- exp(a[i]*(theta-b[i]))/(1+exp(a[i]*(theta-b[i]))) } # binary matrix X <- matrix(NA, nrow=nGene, ncol=nSample) for(i in 1:nSample){ X[, i] <- rbinom(nGene, size=1, prob=P[, i]) } # IRT fitting fit2PL <- fitOnSinglePlat(X, model=3) dffclt <- coef(fit2PL$fit)[, 'Dffclt'] dscrmn <- coef(fit2PL$fit)[, 'Dscrmn'] # estimated latent trait score <- computeAbility(X, dffclt=dffclt, dscrmn=dscrmn) ```

computeAbility function