Data for assessing the contribution of non-verbal IQ to children's reading skills in dyslexic and non-dyslexic children.

1 | ```
data("ReadingSkills")
``` |

A data frame containing 44 observations on 3 variables.

- accuracy
reading score scaled to the open unit interval (see below).

- dyslexia
factor. Is the child dyslexic? (A sum contrast rather than treatment contrast is employed.)

- iq
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 http://psychology3.anu.edu.au/people/smithson/details/betareg/betareg.html

Cribari-Neto, F., and Zeileis, A. (2010). Beta Regression in R.
*Journal of Statistical Software*, **34**(2), 1–24.
http://www.jstatsoft.org/v34/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.
http://www.jstatsoft.org/v48/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*Unpublished manuscript*, The Australian National University, Canberra.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.

`betareg`

, `MockJurors`

, `StressAnxiety`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
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 details
``` |

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