R: Several indices of the unidimensionality of a set of...

unidim {psych} | R Documentation

## Several indices of the unidimensionality of a set of variables.

### Description

There are a variety of ways of assessing whether a set of items measures one latent trait. `unidim` is just one more way. If a one factor model holds in the data, then the factor analytic decomposition F implies that FF' should reproduce the correlations with communalities along the diagonal. In this case, the fit FF' should be identical to the correlation matrix minus the uniquenesses. unidim is just the ratio of these two estimates. The higher it is, the more the evidence for unidimensionality.

### Usage

    unidim(x, keys.list = NULL, flip = FALSE)

### Arguments

`x` | An input matrix or data frame. If x is not a correlation matrix, then the correlations are found.
`keys.list` | If specified, then a number of scales can be tested at once. (See `scoreItems` for a similar procedure.)
`flip` | If TRUE, then items will be keyed based upon their loadings on the first factor. Automatically done if key.list is NULL.

### Details

This is an exploratory index that is still under development. A number of test cases suggest that it provides high values when the data are in fact unidimensional, low values when they are not.

### Value

`uni.orig` | The raw value of the unidimensional criterion

`alpha` | Standardized alpha of the keyed items (after appropriate reversals)
`av.r` | The average interitem correlation of the keyed items.
`raw.model` | The ratio of the FF' model to the sum(R)
`adj.model` | The ratio of the FF' model to the sum(R) when items are flipped.

itemraw.totalThe ratio of the sum(R - uniqueness)/sum(R) itemadj.totalSame ratio with flipped items

### Note

Still an exploratory statistic. Treat with appropriate caution.

### Author(s)

William Revelle

### See Also

`fa` for factor analysis, `omega` for reliability.

### Examples

    #test the unidimensionality of the five factors of the bfi data set.

    keys.list <-
      list(agree=c("-A1","A2","A3","A4","A5"),conscientious=c("C1","C2","C3","-C4","-C5"),
    extraversion=c("-E1","-E2","E3","E4","E5"),neuroticism=c("N1","N2","N3","N4","N5"),
    openness = c("O1","-O2","O3","O4","-O5"))
    unidim(bfi,keys.list)

    #Try a known 3 factor structure
    x <- sim.minor(nfact=3,bipolar=FALSE)
    unidim(x$model)
    keys.list <- list(first =c(1:4),second = 5:8,third=9:12,all=1:12)
    unidim(x$model,keys.list)

    x <- sim.minor(nfact=3)
    unidim(x$model,keys.list,flip=TRUE)

[Package psych version 1.7.3.21 Index]