Dyslexia and IQ Predicting Reading Accuracy
Data for assessing the contribution of non-verbal IQ to children's reading skills in dyslexic and non-dyslexic children.
data("ReadingSkills")A data frame containing 44 observations on 3 variables.
reading score scaled to the open unit interval (see below).
factor. Is the child dyslexic? (A sum contrast rather than treatment contrast is employed.)
non-verbal intelligence quotient transformed to z-scores.
The data were collected by Pammer and Kevan (2004) and employed by
Smithson and Verkuilen (2006). The original reading accuracy score was transformed
by Smithson and Verkuilen (2006) so that accuracy is in the open unit
interval (0, 1) and beta regression can be employed. First, the original accuracy
was scaled using the minimal and maximal score (a and b, respectively)
that can be obtained in the test: (original_accuracy - a) / (b - a)
(a and b are not provided). Subsequently, the scaled score is transformed
to the unit interval using a continuity correction: (scaled_accuracy * (n-1) - 0.5) / n
(either with some rounding or using n = 50 rather than 44).
Example 3 from Smithson and Verkuilen (2006) supplements.
Cribari-Neto, F., and Zeileis, A. (2010). Beta Regression in R. Journal of Statistical Software, 34(2), 1–24. doi: 10.18637/jss.v034.i02
Grün, B., Kosmidis, I., and Zeileis, A. (2012). Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned. Journal of Statistical Software, 48(11), 1–25. doi: 10.18637/jss.v048.i11
Pammer, K., and Kevan, A. (2004). The Contribution of Visual Sensitivity, Phonological Processing and Non-Verbal IQ to Children's Reading. Unpublished manuscript, The Australian National University, Canberra.
Smithson, M., and Verkuilen, J. (2006). A Better Lemon Squeezer? Maximum-Likelihood Regression with Beta-Distributed Dependent Variables. Psychological Methods, 11(7), 54–71.
data("ReadingSkills", package = "betareg")
## Smithson & Verkuilen (2006, Table 5)
## OLS regression
## (Note: typo in iq coefficient: 0.3954 instead of 0.3594)
rs_ols <- lm(qlogis(accuracy) ~ dyslexia * iq, data = ReadingSkills)
summary(rs_ols)
## Beta regression (with numerical rather than analytic standard errors)
## (Note: Smithson & Verkuilen erroneously compute one-sided p-values)
rs_beta <- betareg(accuracy ~ dyslexia * iq | dyslexia + iq,
data = ReadingSkills, hessian = TRUE)
summary(rs_beta)
## visualization
plot(accuracy ~ iq, data = ReadingSkills, col = as.numeric(dyslexia), pch = 19)
nd <- data.frame(dyslexia = "no", iq = -30:30/10)
lines(nd$iq, predict(rs_beta, nd))
lines(nd$iq, plogis(predict(rs_ols, nd)), lty = 2)
nd <- data.frame(dyslexia = "yes", iq = -30:30/10)
lines(nd$iq, predict(rs_beta, nd), col = 2)
lines(nd$iq, plogis(predict(rs_ols, nd)), col = 2, lty = 2)
## see demo("SmithsonVerkuilen2006", package = "betareg") for more detailsPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.