md_15.1: Data 15.1 / 11.5 from Maxwell & Delaney

In afex: Analysis of Factorial Experiments

Description

Hypothetical IQ Data from 12 children at 4 time points: Example data for chapter 11/15 of Maxwell and Delaney (2004, Table 15.1, p. 766) in long format. Has two one within-subjects factor: time.

Usage

md_15.1

Format

A data.frame with 48 rows and 4 variables.

Details

Description from pp. 534:

The data show that 12 subjects have been observed in each of 4 conditions. To make the example easier to discuss, let's suppose that the 12 subjects are children who have been observed at 30, 36, 42, and 48 months of age. In each case, the dependent variable is the child's age-normed general cognitive score on the McCarthy Scales of Children's Abilities. Although the test is normed so that the mean score is independent of age for the general population, our 12 children may come from a population in which cognitive abilities are either growing more rapidly or less rapidly than average. Indeed, this is the hypothesis our data allow us to address. In other words, although the sample means suggest that the children's cognitive abilities are growing, a significance test is needed if we want to rule out sampling error as a likely explanation for the observed differences.

To replicate the results in chapter 15 several different contrasts need to be applied, see Examples.

time is time in months (centered at 0) and timecat is the same as a categorical variable.

Author(s)

R code for examples written by Ulf Mertens and Henrik Singmann

Source

Maxwell, S. E., & Delaney, H. D. (2004). Designing experiments and analyzing data: a model-comparisons perspective. Mahwah, N.J.: Lawrence Erlbaum Associates. p. 766

Examples

### replicate results from Table 15.2 to 15.6 (Maxwell & Delaney, 2004, pp. 774)
data(md_15.1)

### ANOVA results (Table 15.2)
aov_4(iq ~ timecat + (timecat|id),data=md_15.1, anova_table=list(correction = "none"))

### Table 15.3 (random intercept only)
# we need to set the base level on the last level:
contrasts(md_15.1$timecat) <- contr.treatment(4, base = 4)
# "Type 3 Tests of Fixed Effects"
(t15.3 <- mixed(iq ~ timecat + (1|id),data=md_15.1, check.contrasts=FALSE))
# "Solution for Fixed Effects" and "Covariance Parameter Estimates"
summary(t15.3$full.model)

### make Figure 15.2
plot(NULL, NULL, ylim = c(80, 140), xlim = c(30, 48), ylab = "iq", xlab = "time")
plyr::d_ply(md_15.1, plyr::.(id), function(x) lines(as.numeric(as.character(x$timecat)), x$iq))

### Table 15.4, page 789
# random intercept plus slope
(t15.4 <- mixed(iq ~ timecat + (1+time|id),data=md_15.1, check.contrasts=FALSE))
summary(t15.4$full.model)

### Table 15.5, page 795
# set up polynomial contrasts for timecat
contrasts(md_15.1$timecat) <- contr.poly
# fit all parameters separately
(t15.5 <- mixed(iq ~ timecat + (1+time|id), data=md_15.1, check.contrasts=FALSE,
                  per.parameter="timecat"))
# quadratic trend is considerably off, conclusions stay the same.


### Table 15.6, page 797
# growth curve model
(t15.6 <- mixed(iq ~ time + (1+time|id),data=md_15.1))
summary(t15.6$full.model)

Example output

Loading required package: lme4
Loading required package: Matrix
Loading required package: lsmeans
Loading required package: estimability
************
Welcome to afex. For support visit: http://afex.singmann.science/
- Functions for ANOVAs: aov_car(), aov_ez(), and aov_4()
- Methods for calculating p-values with mixed(): 'KR', 'S', 'LRT', and 'PB'
- 'afex_aov' and 'mixed' objects can be passed to lsmeans() for follow-up tests
- Get and set global package options with: afex_options()
- Set orthogonal sum-to-zero contrasts globally: set_sum_contrasts()
- For example analyses see: browseVignettes("afex")
************

Attaching package: 'afex'

The following object is masked from 'package:lme4':

    lmer

Anova Table (Type 3 tests)

Response: iq
   Effect    df   MSE      F ges p.value
1 timecat 3, 33 60.79 3.03 * .06     .04
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
Fitting one lmer() model. [DONE]
Calculating p-values. [DONE]
Mixed Model Anova Table (Type 3 tests, KR-method)

Model: iq ~ timecat + (1 | id)
Data: md_15.1
   Effect    df      F p.value
1 timecat 3, 33 3.03 *     .04
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
Warning message:
'check.contrasts' is deprecated; use 'check_contrasts' instead 
Length  Class   Mode 
     0   NULL   NULL 
Fitting one lmer() model. [DONE]
Calculating p-values. [DONE]
Mixed Model Anova Table (Type 3 tests, KR-method)

Model: iq ~ timecat + (1 + time | id)
Data: md_15.1
   Effect       df    F p.value
1 timecat 3, 22.53 1.72     .19
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
Warning message:
'check.contrasts' is deprecated; use 'check_contrasts' instead 
Length  Class   Mode 
     0   NULL   NULL 
Fitting one lmer() model. [DONE]
Calculating p-values. [DONE]
Mixed Model Anova Table (Type 3 tests, KR-method)

Model: iq ~ timecat + (1 + time | id)
Data: md_15.1
   Effect       df    F p.value
1 timecat 3, 22.53 1.72     .19
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
Warning messages:
1: 'per.parameter' is deprecated; use 'per_parameter' instead 
2: 'check.contrasts' is deprecated; use 'check_contrasts' instead 
Contrasts set to contr.sum for the following variables: id
Numerical variables NOT centered on 0 (i.e., interpretation of all main effects might be difficult if in interactions): time
Fitting one lmer() model. [DONE]
Calculating p-values. [DONE]
Mixed Model Anova Table (Type 3 tests, KR-method)

Model: iq ~ time + (1 + time | id)
Data: md_15.1
  Effect    df      F p.value
1   time 1, 11 5.02 *     .05
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
Length  Class   Mode 
     0   NULL   NULL 

afex documentation built on May 2, 2019, 6:08 p.m.