Prospective Outcomes of Informal and Formal Home Care: Mortality and Institutionalization. APPENDIX A: ORTHOGONAL CODING OF DUMMY VARIABLES

12/19/1990

Dummy variables representing the comparisons are designed by coding one category in each comparison as 1 and the other category as -1. For the five categories of help shown in the following table, four comparisons are possible. To be orthogonal, i.e., uncorrelated, they must fulfill the criteria that the mean of each contrast equals zero and the cross-products of any pair of contrasts equal zero. If the number of cases in each category is equal, then the orthogonal criteria will hold. otherwise the values in the table must be weighted according to the proportion of cases observed in the categories.

Comparison Caregiver Help Category
Without Disability
(1)
Disability Without Help
(2)
With Only Paid Help
(3)
Some Unpaid Help: Family
(4)
Some Unpaid Help: Other
(5)
(A) 1 -1/4 -1/4 -1/4 -1/4
(B) 0 1 -1/3 -1/3 -1/3
(C) 0 0 1 -1/2 -1/2
(D) 0 0 0 1 -1

In comparison (D), for example, if the latter categories have 50 and 25 cases respectively, then the comparison will have weights 2/3 (50/75) and 1/3 (25/75), respectively. Note that [50 cases x 1 (the code) x 1/3 (the weight)] + [25 cases x -1 (the code) x 2/3 (the weight)] = 0. Weights differ depending on the outcome analyzed since the mortality and nursing home data sets differ in number of cases. The weights used in this report are shown in Table A.1 and Table A.2.

TABLE A.1. Weights for Orthogonal Contrasts Among Caregiving Categories: Mortality Data Set
Hypothesis Caregiver Help Category
Without Disability
(1)
Disability Without Help
(2)
With Only Paid Help
(3)
Some Unpaid Help: Family
(4)
Some Unpaid Help: Other
(5)
With Only Unpaid Help
(6)
Some Paid Help: Family
(7)
Some Paid Help: Other
(8)
(0) .7237 -.2763 -.2763 -.2763 -.2763 N/A N/A N/A
(1A) 0 .1322 -.8678 -.8678 -.8678 N/A N/A N/A
(1B) 0 0 .1898 -.8102 -.8102 N/A N/A N/A
(1C) 0 0 0 .6284 -.3716 N/A N/A N/A
(2B) 0 0 N/A N/A N/A .7970 -.2050 -.2050
(2C) 0 0 N/A N/A N/A 0 .4725 -.5275


TABLE A.2. Weights for Orthogonal Contrasts Among Caregiving Categories: Nursing Home Data Set
Hypothesis Caregiver Help Category
Without Disability
(1)
Disability Without Help
(2)
With Only Paid Help
(3)
Some Unpaid Help: Family
(4)
Some Unpaid Help: Other
(5)
With Only Unpaid Help
(6)
Some Paid Help: Family
(7)
Some Paid Help: Other
(8)
(0) .7244 -.2756 -.2756 -.2756 -.2756 N/A N/A N/A
(1A) 0 .1232 -.8768 -.8768 -.8768 N/A N/A N/A
(1B) 0 0 .1869 -.8131 -.8131 N/A N/A N/A
(1C) 0 0 0 .6253 -.3747 N/A N/A N/A
(2B) 0 0 N/A N/A N/A .7968 -.2032 -.2032
(2C) 0 0 N/A N/A N/A 0 .4671 -.5329


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