When constructing scales through rational, factorial, or empirical means, it is useful to examine the content of the items that relate most highly to each other (e.g., the factor loadings of fa.lookup of a set of items) , or to some specific set of criteria (e.g., bestScales). Given a dictionary of item content, these routines will sort by factor loading or criteria correlations and display the item content.
bestScales(x,criteria,cut=.1,n.item =10,overlap=FALSE,dictionary=NULL,check=FALSE,
impute="none", n.iter =1,frac=.9,digits=2)
bestItems(x,criteria=1,cut=.3, abs=TRUE, dictionary=NULL,check=FALSE,digits=2)
lookup(x,y,criteria=NULL)
fa.lookup(f,dictionary,digits=2)
item.lookup(f,m, dictionary,cut=.3, digits = 2)
keys.lookup(keys.list,dictionary)A data matrix or data frame depending upon the function.
A data matrix or data frame or a vector
Which variables (by name or location) should be the empirical target for bestScales and bestItems. May be a separate object.
The object returned from either a factor analysis (fa) or a principal components analysis (principal)
A list of scoring keys suitable to use for make.keys
Return all values in abs(x[,c1]) > cut.
if TRUE, sort by absolute value in bestItems
a data.frame with rownames corresponding to rownames in the f$loadings matrix or colnames of the data matrix or correlation matrix, and entries (may be multiple columns) of item content.
if TRUE, delete items with no variance
A data frame of item means
How many items make up an empirical scale
Are the correlations with other criteria fair game for bestScales
When finding the best scales, and thus the correlations with the criteria, how should we handle missing data? The default is drop missing items.
Replicate the best item function n.iter times, sampling frac of the cases each time, and validating on 1 - frac of the cases.
What fraction of the subjects should be used for the derivation sample. frac is set to one if n.iter = 1
round to digits
bestScales returns the correlation of the empirically constructed scale with each criteria and the items used in the scale. If a dictionary is specified, it also returns a list (value) that shows the item content. Also returns the keys list so that scales can be found using cluster.cor or scoreItems.
bestItems returns a sorted list of factor loadings or correlations with the labels as provided in the dictionary.
lookup is a very simple implementation of the match function.
fa.lookup takes a factor/cluster analysis object (or just a keys like matrix), sorts it using fa.sort and then matches by row.name to the corresponding dictionary entries.
bestScales will find up to n.items that have absolute correlations with a criterion greater than cut. If the overlap option is FALSE (default) the other criteria are not used. This is an example of ``dust bowl empiricism" in that there is not latent construct being measured, just those items that most correlate with a set of criteria. The empirically identified items are then formed into scales (ignoring concepts of internal consistency) which are then correlated with the criteria.
Clearly, bestScales is capitalizing on chance associations. Thus, we can validate the empirical scales by deriving them on a fraction of the total number of subjects, and cross validating on the remaining subjects. This is done n.iter times to show the variability of these empirically derived scale validities. This can only be done if x is a data matrix, not a correlation matrix. For very large data sets (e.g., those from SAPA) these scales seem very stable.
The criteria can be the colnames of elements of x, or can be a separate data.frame.
bestItems and lookup are simple helper functions to summarize correlation matrices or factor loading matrices. bestItems will sort the specified column (criteria) of x on the basis of the (absolute) value of the column. The return as a default is just the rowname of the variable with those absolute values > cut. If there is a dictionary of item content and item names, then include the contents as a two column matrix with rownames corresponding to the item name and then as many fields as desired for item content. (See the example dictionary bfi.dictionary).
lookup is used by bestItems and will find values in c1 of y that match those in x. It returns those rows of y of that match x.
Suppose that you have a "dictionary" of the many variables in a study but you want to consider a small subset of them in a data set x. Then, you can find the entries in the dictionary corresponding to x by lookup(rownames(x),y) If the column is not specified, then it will match by rownames(y).
fa.lookup is used when examining the output of a factor analysis and one wants the corresponding variable names and contents. The returned object may then be printed in LaTex by using the df2latex function with the char option set to TRUE.
Similarly, given a correlation matrix, r, of the x variables, if you want to find the items that most correlate with another item or scale, and then show the contents of that item from the dictionary, bestItems(r,c1=column number or name of x, contents = y)
item.lookup combines the output from a factor analysis fa with simple descriptive statistics (a data frame of means) with a dictionary. Items are grouped by factor loadings > cut, and then sorted by item mean. This allows a better understanding of how a scale works, in terms of the meaning of the item endorsements.
Revelle, W. (in preparation) An introduction to psychometric theory with applications in R. Springer. (Available online at https://personality-project.org/r/book).
# NOT RUN {
bs <- bestScales(bfi,criteria=c("gender","education","age"),dictionary=bfi.dictionary)
bs
f5 <- fa(bfi,5)
m <- colMeans(bfi,na.rm=TRUE)
item.lookup(f5,m,dictionary=bfi.dictionary[2])
fa.lookup(f5,dictionary=bfi.dictionary[2]) #just show the item content, not the source of the items
# }
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