# partwhole: Part-Whole Correlation In multicon: Multivariate Constructs

## Description

Returns the part-whole correlations between an item or the mean of all possible groups of nitems and the composite of the full set of items.

## Usage

 1 partwhole(x, nitems = 1, nomiss = 0.8)

## Arguments

 x A matrix or data.frame containing the variables (in columns) thought to form a composite. nitems A numeric element indicating the number of items desired for each possible group of items. nomiss A numeric between .00 and 1.00 indicating the proportion of scores that must be non-missing for each composite before a score of NA is returned.

## Details

The purpose of this function is to determine which subset of items, when formed into a unit-weighted composite, most strongly correlate with both a unit-weighted and a components weighted composite of the full set of items. For example, if one has an 8 item scale and wants to reduce it to a 4 item scale, it might be interest to know which 4 items can be composited and correlate most highly with the composite from the full set of 8 items. It turns out there are 70 ways to form 4-item composites from 8 total items. This function creates all 70 of those composites and correlates each with both a unit weighted composite from the original 8 items and a components scored (1 principal component) composite of the original 8 items. One can then look at the output to determine which 4-item composite best correlated with the full scale composite.

## Value

A matrix with 2 rows and K columns where K is the number of possible subset combinations. The column names indicate which items (separated by an underline) make up the subset combination. The first row (UnitWgt) is the result using a unit weighted composite for the total set of items and the second row (Component) is the result using principle component scores for the total set of items.

Ryne A. Sherman

## Examples

 1 2 3 4 5 6 7 8 9 10 11 12 13 data(bfi.set) # Imagine we want to find the best two-item composite that correlates # highest with the full 8 items available to measure extraversion. # Three (of the extraversion) items need to be reverse scored sBFI6r <- 6 - bfi.set\$sBFI6 sBFI21r <- 6 - bfi.set\$sBFI21 sBFI31r <- 6 - bfi.set\$sBFI31 # Now put them all into one data.frame ext.vars <- data.frame(bfi.set\$sBFI1, sBFI6r, bfi.set\$sBFI11, bfi.set\$sBFI16, sBFI21r, bfi.set\$sBFI26, sBFI31r, bfi.set\$sBFI36) head(ext.vars) # Looks good # Now compute the parwhole correlation for all possible 2-item composites partwhole(ext.vars, 2)

### Example output

bfi.set.sBFI1 sBFI6r bfi.set.sBFI11 bfi.set.sBFI16 sBFI21r bfi.set.sBFI26
1             5      5              4              4       5              4
2             4      3              5              5       2              3
3             3      2              2              3       2              3
4             4      3              4              4       3              3
5             3      4              4              4       3              4
6             5      3              4              4       4              4
sBFI31r bfi.set.sBFI36
1       5              5
2       1              4
3       2              2
4       2              3
5       2              4
6       4              5
1_2       1_3       1_4       1_5       1_6       1_7       1_8
UnitWgt   0.8442703 0.8220590 0.8345734 0.8707309 0.7998720 0.8458420 0.8538019
Component 0.8375887 0.8381451 0.8495031 0.8688132 0.7984325 0.8384747 0.8666528
2_3       2_4       2_5       2_6       2_7       2_8       3_4
UnitWgt   0.8514361 0.8540545 0.8355492 0.8008026 0.8037861 0.8767012 0.7409587
Component 0.8501461 0.8518743 0.8202961 0.7818108 0.7822599 0.8735861 0.7615846
3_5       3_6       3_7       3_8       4_5       4_6       4_7
UnitWgt   0.9051586 0.7423189 0.8468963 0.8407350 0.8978696 0.7462679 0.8524176
Component 0.9086982 0.7474811 0.8449537 0.8607046 0.9004398 0.7502767 0.8495837
4_8       5_6       5_7       5_8       6_7       6_8       7_8
UnitWgt   0.8303802 0.8603569 0.8394935 0.9104896 0.7904131 0.7961346 0.8517101
Component 0.8486490 0.8474014 0.8234883 0.9119080 0.7707201 0.7987832 0.8480722

multicon documentation built on May 2, 2019, 3:18 a.m.