Distorted correlations among censored data: causes, effects, and correction.

Data censoring occurs when researchers do not know precise values of data points (e.g., age is 55+ or concentration ≤ .001). Censoring is frequent within psychology but typically unrecognized outside of longitudinal studies. We describe five circumstances when censoring may occur, demonstrate censoring distorts correlations, and discuss how censoring can create spurious factors. Next, we explain how to use R package lava to calculate maximum likelihood estimates (Holst and Budtz-Jørgensen Computational Statistics, 28(4), 1385-1452, 2013) of correlations between uncensored variables based upon censored variables. Previous research demonstrated these estimates were more accurate than Muthén's (1984) estimate for one particular model, but no research has systematically examined their accuracy. We therefore conducted a simulation study exploring the effects of the correlation, sample size, and censoring on point and interval estimates of correlations. Based upon 80 cells in which low values of normally distributed variables were censored, we recommend the constrained regression model with Wald confidence intervals. These methods were precise and unbiased unless both variables had 70% censoring and the correlation was large and negative (e.g., -.9), in which case estimates were closer to -1 than they should be. Opposite results would occur if low values of one variable and high values of the other were censored: Estimates would be precise and unbiased unless censoring was extreme and correlations were large and positive. To estimate large correlations accurately, we recommend researchers reduce censoring by using longer longitudinal studies, using scales with more response options, and matching measures to populations to reduce floor and ceiling effects.