statsBy(data, group, cors = FALSE, method="pearson",poly=FALSE)
statsBy.boot(data,group,ntrials=10,cors=FALSE,replace=TRUE,method="pearson")
statsBy.boot.summary(res.list,var="ICC2")
faBy(stats, nfactors = 1, rotate = "oblimin", fm = "minres", free = TRUE, all=FALSE,...)fa for details)statsBy is a much simpler function to give some of the basic descriptive statistics for two level models. It is meant to supplement true multilevel modeling.For a group variable (group) for a data.frame or matrix (data), basic descriptive statistics (mean, sd, n) as well as within group correlations (cors=TRUE) are found for each group.
The amount of variance associated with the grouping variable compared to the total variance is the type 1 IntraClass Correlation (ICC1): $ICC1 = (MSb-MSw)/(MSb + MSw*(npr-1))$ where npr is the average number of cases within each group.
The reliability of the group differences may be found by the ICC2 which reflects how different the means are with respect to the within group variability. $ICC2 = (MSb-MSw)/MSb$. Because the mean square between is sensitive to sample size, this estimate will also reflect sample size.
Perhaps the most useful part of statsBy is that it decomposes the observed correlations between variables into two parts: the within group and the between group correlation. This follows the decomposition of an observed correlation into the pooled correlation within groups (rwg) and the weighted correlation of the means between groups discussed by Pedazur (1997) and by Bliese in the multilevel package.
$r_{xy} = eta_{x_{wg}} * eta_{y_{wg}} * r_{xy_{wg}} + eta_{x_{bg}} * eta_{y_{bg}} * r_{xy_{bg}}$
where $r_{xy}$ is the normal correlation which may be decomposed into a within group and between group correlations $r_{xy_{wg}}$ and $r_{xy_{bg}}$ and eta is the correlation of the data with the within group values, or the group means.
It is important to realize that the within group and between group correlations are independent of each other. That is to say, inferring from the 'ecological correlation' (between groups) to the lower level (within group) correlation is inappropriate. However, these between group correlations are still very meaningful, if inferences are made at the higher level.
There are actually two ways of finding the within group correlations pooled across groups. We can find the correlations within every group, weight these by the sample size and then report this pooled value (pooled). This is found if the cors option is set to TRUE. It is logically equivalent to doing a sample size weighted meta-analytic correlation. The other way, rwg, considers the covariances, variances, and thus correlations when each subject's scores are given as deviation score from the group mean.
If finding polychoric correlations, these two estimates will differ, for the pooled value is the weighted polychoric correlation, but the rwg is the Pearson correlation.
Confidence values and significance of $r_{xy_{wg}}$, pwg, reflect the pooled number of cases within groups, while $r_{xy_{bg}}$, pbg, the number of groups. These are not corrected for multiple comparisons.
withinBetween is an example data set of the mixture of within and between group correlations. sim.multilevel will generate simulated data with a multilevel structure.
The statsBy.boot function will randomize the grouping variable ntrials times and find the statsBy output. This can take a long time and will produce a great deal of output. This output can then be summarized for relevant variables using the statsBy.boot.summary function specifying the variable of interest. These two functions are useful in order to find if the mere act of grouping leads to large between group correlations.
Consider the case of the relationship between various tests of ability when the data are grouped by level of education (statsBy(sat.act,"education")) or when affect data are analyzed within and between an affect manipulation (statsBy(flat,group="Film") ). Note in this latter example, that because subjects were randomly assigned to Film condition for the pretest, that the pretest ICC1s cluster around 0.
faBy uses the output of statsBy to perform a factor analysis on the correlation matrix within each group. If the free parameter is FALSE, then each solution is rotated towards the group solution (as much as possible). The output is a list of each factor solution, as well as a summary matrix of loadings and interfactor correlations for all groups.
describeBy and the functions within the multilevel package.#Taken from Pedhazur, 1997
pedhazur <- structure(list(Group = c(1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
2L), X = c(5L, 2L, 4L, 6L, 3L, 8L, 5L, 7L, 9L, 6L), Y = 1:10), .Names = c("Group",
"X", "Y"), class = "data.frame", row.names = c(NA, -10L))
pedhazur
ped.stats <- statsBy(pedhazur,"Group")
ped.stats
#Now do this for the sat.act data set
sat.stats <- statsBy(sat.act,c("education","gender"),cor=TRUE) #group by two grouping variables
print(sat.stats,short=FALSE)
lowerMat(sat.stats$pbg) #get the probability values
#show means by groups
round(sat.stats$mean)
#Do separate factor analyses for each group
#faBy(sat.stats,1)Run the code above in your browser using DataLab