Reducing Measurement Error in Student Achievement Estimation

Abstract

maximum likelihood estimation, measurement error, Rasch model, teacher grade, SIMEX,

Adjustment of recall errors in duration data using SIMEX

“…]) #I put the mean regression estimates from each level of simulated measurement error in a dataset avg_noiseADJ_cons = NA avg_noiseADJ_X1 = NA avg_noiseADJ_X2 = NA lambda = c(-1, 0, .5, 1, 1.5, 2) addi1 = c(avg_noiseADJ_cons, coef(lm.naive) [1], avg.5_cons, avg1_cons, avg1.5_cons, avg2_cons) addi2 = c(avg_noiseADJ_X1, coef(lm.naive) [2], avg.5_X1, avg1_X1, avg1.5_X1, avg2_X1) addi3 = c(avg_noiseADJ_X2, coef(lm.naive) [3], avg.5_X2, avg1_X2, avg1.5_X2, avg2_X2) SIMEX = data.frame(lambda, addi1, addi2, addi3) names(SIMEX) = c("lambda","cons","X1","X2") #I obtain the adjusted SIMEX estimates using a linear extrapolation function SIMEXna = SIMEX[-1,] SIMEX_cons = lm(SIMEXna$cons ~ SIMEXna$lambda) SIMEX [1,2] = coef(SIMEX_cons) [1] + (-1)*coef(SIMEX_cons) [2] SIMEX_X1 = lm(SIMEXna$X1 ~ SIMEXna$lambda) SIMEX [1,3] = coef(SIMEX_X1) [1] + (-1)*coef(SIMEX_X1) [2] SIMEX_X2 = lm(SIMEXna$X2 ~ SIMEXna$lambda) SIMEX [1,4] = coef(SIMEX_X2) [1] + (-1)*coef(SIMEX_X2) [2] #I save the adjusted estimates and the remaining bias results [1,1] = SIMEX [1,2] results [2,1] = SIMEX [1,3] results [3,1] = SIMEX [1,4] bias1 = SIMEX [1,2]-coef(lm.true) [1] bias2 = SIMEX [1,3]-coef(lm.true) [2] bias3 = SIMEX [1,4]-coef(lm.true) [3] results [1,2] = bias1 results[2,2] = bias2 results …”

“…This is especially true for surveys using a retrospective design, which collect information about past events 1 School of Law, University of Leeds, J.PinaSanchez@leeds.ac.uk from a single contact with respondents. The advantages of retrospective designs, in comparison with prospective studies 2 , are well known: a) immune to problems of attrition; b) cheaper to administer; and c) more capable of detecting transitions occurring in short periods.…”

Structural Modeling of Measurement Error in Generalized Linear Models with Rasch Measures as Covariates

“…This method can be useful when the maximization of the log-likelihood function is problematic, as proposed in Battauz, Bellio and Gori (2008) for ordinal data. The SIMEX method is simple to implement, but it is based on simulation and does not fully exploit the information available on the measurement error structure.…”