COST FUNCTION ANALYSIS OF MINNESOTA INTERMEDIATE CARE FACILITIES FOR MENTALLY
RETARDED ( ICF-MR) PER DIEMS
I. INTRODUCTION
The direction and magnitude of reinstitutionalization may be determined in the
future by cost arguments at both the national and state levels. The recent Welsch v. Noot Consent Decree (1980) makes it especially imperative that policymakers identify and examine the many factors which affect the cost of community residential care in Minnesota. Future research will examine the total system costs for state hospitals and community programs, projected costs for alternative types of living arrangements, and the efficacy of
existing funding mechanisms.
The primary purpose of the present study is to identify the critical factors (separately and in combination) which produce variations in per diem costs in Intermediate Care Facilities for Mentally Retarded (ICF-MR). The population frame included all ICF-MRS in Minnesota (N = 185) for which reliable data were available. (The most recent data. available from the Department of Public Welfare and the Department of Health were for late 1979; the reader is cautioned about using information from this report for other purposes. A cost function analysis using 1980 data is forthcoming.)
Data for this study were compiled from several sources. The primary sources include:
facility characteristics, per diems and staffing patterns from Rule 52 Cost Reports and computer listings on file in the Audit Division of the Department of Public Welfare;
years of operation and client population (adult or children) from ICF-MR files in the Licensing Division/DPW;
resident characteristics, functioning levels and the type of facility license (Class A or Class B) from Quality Assurance and Review program reports, Minnesota Department of Health.
II. METHODOLOGY
The statistical methodology employed in this study is a replication of the cost
function analysis component of a national study on the costs of residential care (Wieck and Bruininks, 1980). That report contains a thorough review of literature of previous cost studies and a discussion of the "theory" which underlies this study's treatment of cost-related variables.
DEVELOPMENTAL DISABILITIES PLANNING . DEPARTMENT OF ENERGY, PLANNING AND DEVELOPMENT
201 CAPITOL SQUARE BLDG. 550 CEDAR STREET ST. PAUL, MN 55101 l 612/296-4018
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September 30, 1981
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This study, like all statistical analysis, is not definitive. Statistical techniques cannot "prove" cause-effect relationships. They can, however, help policy-makers to estimate/predict cause-effect relationships with greater reliability; hence to make better decisions about allocating scarce resources. The present study attempts to identify several factors and their probable impact upon ICF-MR per diem rates. One important caveat: data derived from DPW files may represent the reimbursement structure rather than "true" cost.
That is, not all "costs" of operation are necessarily reimbursable; not all costs are quantifiable in terms of dollars, although they are costs of operation nonetheless.
III. ANALYSIS OF VARIANCE
The first objective of this study is to test hypotheses about the relationship of selected locational, organizational, and resident characteristic variables with cost. These hypotheses, and results, are summarized as follows:
Locational Factors 1. Ho 1 : There are no differences in the per diem rates for community residential services between Minnesota's eleven economic development regions.
1. According to the results of a one-way analysis of variance test, there were
significant differences (p < .01)2 in the per diem rates of the ICF-MRS located in
the various economic development regions. The ICF-MRS located in the Minneapolis-Saint Paul metropolitan area (Region 11) were operating during " 1979 at the highest mean rate ($44.11), while the ICF-MRS in Regions 6 and 1 were operating at the lowest mean rate ($31.50 and $31.84 respectively). The mean per diem rate for ICF-MRS located in the metropolitan region was significantly different (p < .01) from the mean per diems of all other regions. The analysis of variance and table of means and standard deviations appear
in Tables 1 and 2 respectively.3
1. There are actually 13 economic development regions within the state. For the purposes of this study, Regions 6E and 6W were combined and treated as a single
economic development region (Region 6); likewise for Regions 7E and 7W (Region
7). See the Appendix for a map of the State's economic development regions.
2. The F-test is a statistical measure of the degree of variation among Statistical groups.
The larger the F-score, the smaller the probability that variation among the groups is statistically equal. A "significant" F-score indicates that I there is a large probability (usually 95 percent or more) that a quantifiable statistical difference exists among groups.
3. The "Mean" (z) is a common measure of the central tendency of several variables. It is often referred to as the "average."
Variance (u2) is a measure of the dispersion of the data about the mean; it is a way of measuring how the individual per diems "cluster" around the mean value. The variance will be small where the per diems are very similar. The primary goal of this report is to identify and "explain" variations in per diem rates, i.e., identify those factors which are likely to "cause" differences in per diem rates.
Standard Deviation (u/SD) is another measure of variance. It is a more obvious and
intuitive measure of variation than is Variance because it is based upon the same
units as the original variable (in this case, dollars).
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Table 1
Summary of Analysis of Variance of Minnesota ICF-MR
Per Diems by Region
Source of Variation
df
S
MS
FL
Between Groups 10
3978.56 397.86 3.78**
Within Groups 174 18323.76 105.31
Total 184 22302.32
**p <.01
Table 2
Mean Per Diems of ICF-MRS by Region
Region
Mean
SD
N
Region 1
31.84
8.51
7
Region 2
32.90
3.52
4
Region 3 (Duluth)
35.20
6.64
24
Region 4 (Moorhead)
35.97
10.62
18
Region 5
35.03
.19
2
Region 6
31.50
10.55
7
Region 7 (St. Cloud)
32.76
7.55
14
Region 8
40.18
11.35
8
Region 9 (Mankato)
37.77
7.28
8
Region 10 (Rochester)
38.39 9.26
18
Region 11 (Mpls. -St. Paul)
44.11
12.05
75
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A second one-way analysis of variance was run between those facilities located in
the Minneapolis-Saint Paul region (which contained approximately one half of the State's population and 42 percent of all ICF-MRS in 1979) and all facilities located outside of the seven county metropolitan area. There was a significant difference (p < .01) between metropolitan per diems (%= $44. 11) and Out-State, non-metropolitan per diems
( x = $35,56).
The data contained in this study have not been adjusted in advance for
cost of-living differences which may exist among the regions. Adjustment indices are published for national census regions for a hypothetical family of four in an urban area, but are rarely published for measuring within-state variation. The reader is advised that differences in ICF-MR per diems, although statistically significant, may indeed be indicative of cost-of-living differences rather than "real" cost differences.
Organizational Factors
Eight organizational factors have been suggested in previous studies (Wieck &
Bruininks, 1980) as affecting cost differences: (1) size, (2) ownership of facility, (3) membership in a system or chain of residential facilities under one general ownership, (4) occupancy rate, (5) number of staff, (6) staff-resident ratio, (7) years of operation, and (8) the type of license (Class A or Class B). Estimates of staff turnover were not available for
this analysis.
2. H02: There is no relationship between per diem rates of residential services and facility size (size is defined in terms of number of residents).
Facilities were grouped into five size categories: (1) six or fewer residents, (2) seven to 12 residents, (3) 13 to 16 residents, (4) 17 to 32 residents, and (5) 33 or more residents. There were significant differences (p < .05) in the per diem rates of community residential facilities according to these size categories. The highest per diems were associated with the larger facilities ($42.13/33 or more residents) and the smallest facilities ($41.08/six or fewer residents). The lowest per diem ($35.55) was reported by facilities that had seven to 12 residents. The specific comparisons that produced significant differences (p <.01) were facilities in group 2 with groups 1, 4 and 5; and group 3 with groups 1, 4 and 5. All other comparisons were not significant.
The analysis of variance and table of means and standard deviation appear in Tables
3 and 4 respectively.
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Table 3
Summary of Analysis of Variance of Minnesota
ICF-MR Per Diems by Size Categories
Source of Variation
df
Ss
MS
F
Between Groups
4
1299.90 324.97 2.78*
Within Groups 180 21002.42 116.68
Total
184 22302.32
*p <.05
Table 4
Mean Per Diems of Minnesota ICF-MRS
by Size Categories
Size Categories
Mean
SD
N
Group 1: 6 residents or fewer 41.08 6.89 64
Group 2: 7 - 12 residents 35.55 8.63 49
Group 3: 13 - 16 residents 36.66 11.95 27
Group 4: 17 - 32 residents 39.77 14.64 16
Group 5: 33 or more residents 42.13 16.37 29
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An inverse relationship between size and per diem (cost) is commonly assumed, that is, as size increases per diem decreases. Traditional economic theory suggests,
however, that there is a U-shaped relationship between average cost and size, with
very small or very large facilities incurring higher average costs. Economy of scale may be more easily achieved within mid-size facilities; these economies may be reflected in lower average costs.
Wieck and Bruininks' national study (1980) indicated that there was a positive
relationship between size and per diem: as the size of facilities increases, per
diems increase. This relationship may be attributed to the increased amount of services typically provided by larger facilities. The results of this study suggest that the effects of economy of scale can be greatly affected by such factors as resident characteristics, staff-resident ratio, etc. In order to make meaningful statements about size and per diems,
the issue must be studied longitudinally.
3. H03: There is no relationship between per diem rates of residential services and ownership of facility.
Table 5 presents a summary of the analysis of variance (see Table 6 for means and
standard deviations) for type of legal ownership with per diem as the dependent variable. These results indicate that, unlike nursing homes and community residential facilities in several national studies, the proprietary facilities in Minnesota are operating at higher per diems ($40.22) than non-profit facilities ($38.05); the difference is not statistically significant, however.
Table 5
Summary of Analysis of Variance of Minnesota
ICF-MRS by Profit/Nonprofit Ownership
Source of Variation
df
Ss
MS
F
Between Groups 1 216.65 216.65 1.80
Within Groups 183 22085.66 120.69
Total 184 22302.32
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Table 6
Mean Per Diems of Minnesota ICF-MRS by
Profit/Nonprofit Ownership
Type Mean
SD
N
Proprietary $40.22 12.03 83
Non-profit $38.05 10.06 102
In follow-up to this analysis, a one-way analysis of variance was run comparing
facilities that are "family owned and operated" with those that are not. Wieck and Bruininks (1980) reported that on a national level "family-owned and operated facilities operated at a much lower rate than non-profit facilities...and proprietary facilities"
(p. 136). A similar result occurred in this study, with significant differences (p <.01) occurring between family owned and operated facilities ($34.22) and those that were not ($41.00). Tables 7 and 8 present the summary of the analysis of variance test and the table of means and standard deviations.
Table 7
Summary of Analysis of Variance of Minnesota ICF-MR
Per Diems by Family Ownership
Source of Variation
df
Ss
MS
F
Between Groups
1 1756.65 1756.65 15.65**
Within Groups 183 20545.67 112.27
Total 184 22302.32
**p<.ol
Table 8
Mean Per Diems of Minnesota ICF-MRS
by Family Ownership
Type
Mean
SD
N
Family Owned and Operated
34.22
8.15
54
Non-Family Owned and Operated 41.00 11.44 131
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4. H04: There is no relationship between per diem rates of residential services and membership in a system. (A system is a group of residential facilities owned and operated by one parent organization. )
Significant differences (p < .05) were found between community residential
facilities that were members of systems and those that were not. The average per diem of system ICF-MRS was $40.52; and $36.87 for those that were not affiliated with a system. Tables 9 and 10 present the analysis of variance and table of means and standard deviations respectively.
These results corroborate the finding of Wieck and Bruininks' national study (1980). Further examination of this issue appears necessary before meaningful conclusions can be drawn.
Table 9
Summary of Analysis of Variance of Minnesota ICF-MR
Per Diem by System Membership
Source of Variation df
Ss
MS
F
Between Groups 1 598.40 598.40 5.045*n
Within Groups 183 21703.92 118.60
Total 184 22302.32
*p <.05
Table 10
Mean Per Diem of ICF-MRS by System Membership
Type
Mean
SD
N
Member of System $40.52 9.14 109
Non-member of System $36.87 13.00 76
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5. H05: There is no relationship between per diem rates of residential services and occupancy rate.
Occupancy rate was defined as the number of residents divided by the licensed bed
capacity. Occupancy ranged from less than 80 percent to 100 percent. The rates were categorized as follows: (1) 80 percent or less, (2) 81 to 90 percent, (3) 91 to 95 percent, and (4) 96 to 100 percent.
Previous studies have suggested that substantial variation in occupancy rates has
had important consequences for cost, primarily because per diem is calculated on the number of residents (Peat, MarWick, Mitchell, & Co., 1976; Piasecki, Pittinger, & Rutman, 1977). ICF-MRS in Minnesota typically operate at or near licensed capacity.
During 1979, nearly 84 percent of the facilities (N = 155) were operating at more than 95 percent of their licensed capacity.
No significant differences were found in comparing means of facilities grouped by
occupancy rates, although facilities with occupancy rates of 81 to 90 percent had the highest per diem ($43.56). Tables 11 and 12 present the analysis of variance and table of means and standard deviations, respectively.
Table 11
Summary of Analysis of Variance of Minnesota ICF-MR
Per Diems by Occupancy Rate
Source of Variation
df
Ss
MS
F
Between Groups 3 424.70 141.57 1.117
Within Groups 181 21877.62 120.87
Total 184 22302.32
Table 12
Mean Per Diems of ICF-MRS by Occupancy Rate
Occupancy Rate
Mean
SD
N
Group 1: g80% $34.73 1.38 4
Group 2: 81-90%
$43.56 16.73 11
Group 3: 91-95% $36.15 11.59 15
Group 4: 96 - 100% $39.09 10.57 155
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6. HOG: There is no relationship between per diem rates of residential services and number of staff.
A Pearson correlation coefficient was calculated between the number of full-time equivalent (FTE) direct care staff and per diem rates. The number of direct care staff was positively correlated (r = .39) at a significant level (p < .01).
7. H07: There is no relationship between per diem rates of residential services and staff-resident ratio.
The staff-resident ratio factor illustrates the difficulty of identifying cause-effect relationships within residential care organizations. Resident ratio, resident characteristics and facility services--as well as "artificial" conditions created by rules and regulations--appear to be highly correlated.
There is considerable evidence to suggest that staff-resident ratio is very much
related to an organization's per diem rate. Residential services are labor-intensive industries; consequently, any change in the number or wage structure of employees will have a substantial impact upon costs.
In this study, the staff-resident ratio was calculated for each facility by dividing the total number of full-time equivalent direct care staff (40 hour week) by the total number of residents. The staff-resident ratios were categorized into five groups: (1) less than .33,
(2) .33 to .65, (3) .66 to .99, (4) 1.00 to 1.32, and (5) 1.33 or more. A one-way analysis of variance was run with significant differences (p < .01) found among these groups.
Examination of the table of means (Table 14) indicates a direct relationship between staff-resident ratios and per diem costs: the higher the staff-resident ratio, the higher the per diem. When comparing each group with all others, only one comparison was not significant; that was group number one ($36.49) with group number two ($37.32). Table 13 presents the analysis of variance summary.
Table 13
Summary of Analysis of Variance of Minnesota ICF-MR
Per Diems by Staff-Resident Ratio
Source of Variation
df
Ss
MS
F
Between Groups 4 5551.59 1387.90 14.9*
Within Groups 180 16750.73 93.06
Total
184 22302.32
**p <.01
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Table 14
Mean Per Diems of ICF-MRS by Staff-Resident Ratio
Staff-Resident Ratio
Mean
SD
N
Group 1: < .33 $36.49 10.97 83
Group 2: .33-.65
$37.32 6.31 63
Group 3: .66-.99 $42.56 10.41 28
Group 4: 1.00 - 1.32 $56.61 11.69 8
Group 5: 1.33+ $64.92 16.26 3
8. H08: There is no relationship between per diem rates of residential services and years of operation.
It is not uncommon for newly-opened facilities to experience disproportionately
high costs as a result of start-up expenses. Piasecki , et al (1977) suggested that initial costs for establishing a group home may equal or exceed the programs' annual operating budget; these costs might be attributed to building or remodeling requirements, legal fees, personnel recruitment and training or furnishings, supplies and related services.
The year of opening for the facilities was obtained from the Department of Public
Welfare and subtracted from the constant year 1979 - the year from which data were derived. The years of operation were categorized into five groups: (1) one to two years, (2) three to four years, (3) five to six years, (4) seven to 20 years, and (5) 21 years or more. A one-way analysis of variance was calculated with significant differences (p < .01) occurring among groups. The highest per diem ($45.15) was reported for those
facilities which had been operating for less than two years. The lowest mean Per diem
($33.73) was associated with facilities which had been operating for seven to 20 years. The post hoc comparisons between each group with every other group revealed significant differences for all combinations except group three and group four, which was not significant. Tables 15 and 16 present the analysis of variance summary and the table of means and standard deviations.
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Table 15
Summary of Analysis of Variance of Minnesota ICF-MR
Per Diems by Years of Operation
Source of Variation
df
Ss
MS
F
Between Groups 4 2654.35 663.59 6.127**
Within Groups 178 19277.39 108.30
Total 182 21931.74
** p <.01
Table 16
Mean Per Diems of ICF-MRS by Years of Operation
Number of Years
Mean SD N
Group 1: 1-2 years $45.15 12.12 35n
Group 2: 3-4 years $39.98 9.86 67
Group 3: 4-6 years $36.34 10.98 46
Group 4: 7-20 years $33.73 8.34 30
Group 5: 21 years or more $34.28 10.38 5
9. Hog: There is no relationship between per diem rates of residential services and the type of license (Class A and Class B).
ICF-MRS in Minnesota are licensed as either Class A or Class B facilities. The
classifications are dependent upon the residents' self-preservation skills (i.e., ability to egress from the building during an emergency). Class B facilities are for those persons who do not possess self-preservation skills. A one-way analysis of variance was run with significant differences (p < .01) reported for Class B facilities ($54.55) as compared to Class A facilities ($37. 14). Tables 17 and 18 present the analysis of variance summary and the tables of means and standard deviations respectively.
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Table 17
Summary of Analysis of Variance of Minnesota ICF-MR
Per Diems by Class A - Class B Categories
Source of Variation
df
Ss
Its
F
Between Groups 1 5390.94 5390.94 58.63**
Within Groups 180 16550.83 91.95
Total 181 21941.77
**p <.01
Table 18
Mean Per Diems of ICF-MRS by Class A - Class !3 categories
Type Mean SD
N
Class A $37.14 8.45 162
Class B $54.55 16.31 20
Resident Factors
There are six variables related to personal characteristics: (1) proportion of residents with severe or profound mental retardation, (2) proportion of residents who must be completely fed, (3) proportion of non-ambulatory residents, (4) proportion of residents with severe behavior problems, (5) proportion of residents not toilet trained, and (6) age of residents.
10. HO 10: There is no difference in the per diem rates of residential services and the proportion of severely or profoundly mentally retarded residents.
The proportion of residents who were classified as severely or profoundly mentally
retarded was calculated for each facility. These proportions were then categorized into seven groups: (1) zero to five percent, (z) six to nine percent, (3) 10 to 19 percent, (4) 20 to 39 percent, (5) 40 to 49 percent, (6) 50 to 74 percent, and (7) 75 to 100 percent. A one-way analysis revealed significant differences (p < .05) with the lowest per diem ($32.99)
reported for those facilities serving 40 to 49 percent severely or profoundly mentally retarded residents. This particular group differed significantly (p < .01) with all other groups. The analysis of variance summary and table of means and standard deviations appear in Tables 19 and 20 respectively.
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Table 19
Summary of Analysis of Variance of Minnesota ICF-MR Per Diem by Proportion
of Severely or Profoundly Mentally Retarded Residents Served
Source of Variation
df
SS
MS
F
Between Groups 6 1922.78 320.46 2.875*
Within Groups 177 19726.89 111.45
Total 183 21649.67
*p <.05
Table 20
Mean Per Diems of Minnesota ICF-MRS by Proportion of Severely or Profoundly Mentally Retarded Residents Served
Proportion Mean SD N
Group 1: O-5% $39.46 10.22 31
Group 2: 6-9% $39.93 15.98 7
Group 3: 10-19% $44.11 18.22 8
Group 4: 20-39% $37.71 7.69 44
Group 5: 40-49% $32.99 6.74 23
Group 6: 50-74% $37.65 10.03 36
Group 7: 75-100% $43.58 12.91 35
11. Ho 11: There is no difference in the per diem rates of residential services and the proportion of residents who are not ambulatory.
Again, resident data that is non-ambulation from the Department of Health and classified into three groups: (1) zero to five percent, (2) six to nine percent, (3) ten to 19 percent, (4) 20 to 39 percent, (5) 40 percent or more. Significant differences (p<.01) were found when a one-way analysis of variance was run on the various group means. There was a positive relationship between proportion of residents who were completely fed and the per diems. Almost all of the ICF-MRS (N = 175) had a low proportion (zero to 5 Percent) of residents who had to be completely fed. Table 21 presents the analysis of variance summary while Table 22 presents the table of means and standard deviations.
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Table 21
Summary of Analysis of Variance of Minnesota ICF-MR Per Diems by Proportion of
Residents Completely Fed
Source of Variation
df
Ss
Ms
F
Between Groups 4 4927.23 1231.81 12.76**
Within Groups 180 17375.09 96.52
Total 184 22302.32
**p <.01
Table 22
Mean Per Diems of Minnesota ICF-MRS by Proportion of Residents Completely Fed
Proportion
Mean
SD
N
Group 1: O - 5% $37.86 9.41 175
Group 2: 6 - 9% $49.38 12.68 2
Group 3: 10- 19% $51.02 0 1
Group 4: 20 - 39% $60.19 19.50 5
Group 5: 40%+ $71.38 17.08 2
12. H012: There is no difference in the per diem rates of residential services and the proportion of residents who are non-ambulatory
Again, resident data on non-ambulation were obtained from the Department of Health and classified into three groups: (1) zero to nine percent, (2) ten to 19 percent, and (3) 20 to 39 percent. Significant differences (p < .01) were found among groups as shown in Table 23. As the proportion of non-ambulatory residents increases, so does the per diem (as shown in Table 24); with the lowest per diem ($37,72) for facilities with zero to nine percent non-ambulatory residents and the highest per diem ($61.95) for facilities with 20
to 39 percent non-ambulatory residents.
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Table 23
Summary of Analysis of Variance of Minnesota ICF-MR Per Diems
by Proportion of Residents Who are Non-ambulatory
Source of Variation
df
SS
MS
F
Between Groups 2 5243.71 2621.86 27.973**
Within Groups 182 17058.61 93.73
Total 184 22302.32
*p < .01
Table 24
Mean Per Diems of Minnesota ICF-MRS by Proportion
of Residents Who are Non-ambulatory
Proportion
Mean
SD
N
Group 1: O - 9% $37.72 9.24 174
Group 2: 10- 19% $49.37 12.68
2
Group 3: 20- 39% $61.95 16.33 9
13. H013: There is no difference in the per diem rates of residential services and the proportion of residents who have severe behavior problems. Facilities were classified into three groups by proportion of residents who have severe behavior problems (defined by the Department of Health as "uncooperative, wanders, withdrawn, crying, hallucinates, disruptive/runs away...assaultive"): (1) zero to nine percent, (2) ten to 19 percent, and
(3) 20 percent or more.
Significant differences (p < .01) in per diems were revealed when a one-way
analysis of variance was run. The highest per diems ($51.21) were associated with facilities in which 20 percent or more of the residents were classified as having severe behavior problems. Tables 25 and 26 present the analysis of variance summary and tables of means and standard deviations.
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Table 25
Summary of Analysis of Variance of Minnesota ICF-MR Per Diems
by Proportion of Residents with Behavior Problems
Source of Variation
df
SS
MS
F
Between Groups 2 1754.57 877.29 7.77**
Within Groups 182 20547.74 112.9
Total 184 22302.32
1
* p <.01
Table 26
Mean Per Diems of Minnesota ICF-MRS by Proportion
of Residents with Behavior Problems
Proportion
Mean
SD
N
Group 1: 0 - 9% $36.78 8.91 150
Group 2: 10 - 19% $38.89 9.90 25
Group 3: 20%+ $51.21 15.15 10
14. Ho14: There is no difference in the per diem rate of residential services and the proportion of residents who are not toilet trained.
Facilities were grouped according to the proportion of residents who were not
toilet trained: (1) zero to five percent, (2) six to 19 percent, and (3) 20 percent or more.
A one-way analysis of variance revealed significant differences (p < .01) in group per diems with the highest per diem ($59.47) reported for facilities with 20 percent or more residents who were not toilet trained. The summary of the analysis of variance and tables of means and standard deviations appear in Tables 27 and 28 respectively.
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Table 27
Summary of Analysis of Variance of Minnesota ICF-MR Per Diems
by Proportion of Residents Not Toilet Trained
Source of Variation
df
SS
MS
F
Between Groups 2 3689.85 1844.93 18.04*
Within Groups 182 18612.46 102.27
Total 184 22302.32
**p < .01
Table 28
Mean Per Diems of Minnesota ICF-MRS by Proportion
of Residents Not Toilet Trained
Proportion
Mean
SD
N
Group 1: O - 5% $37.92 9.41 174
Group 2: 6- 19% $52.95 22.11 5
Group 3: 20%+ $59.47 16.37 6
15. H015: There is no difference in the per diem rates of residential services and the age of residents served.
The last one-way analysis of variance test was run on four categories of residential facilities grouped by age of residents: (1) zero to 12 years, (2) 13 to 20 years, (3) 21 to 40 years, and (4) 41 years or more. Significant differences were indicated. The highest costs ($51.16) were associated with children's facilities; the lowest costs ($33.57) were associated with ICF-MRS serving older populations (41 years or more).
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Table 29
Summary of Analysis of Variance of Minnesota ICF-MR
Per Diems by Age of Residents
Source of Variation
df
SS
MS
F
Between Groups 3 3243.96 1081.32 10.269**
Within Groups 181 19058.36 105.29
Total 184 22302.32
**p <.01
Table 30
Mean Per Diems of Minnesota ICF-MRS by Age of Residents
Proportion
Mean
SD
N
Group 1: O - 12 years $51.16 15.74 9
Group 2: 13 - 20 years $44.18 11.92 28
Group 3: 21 - 40 years $38.65 10.17 109
Group 4: 41+ years $33.57 7.38 39
IV. COST FUNCTION ANALYSIS
The second objective of this study will be development of an explanation of cost relationships using a cost function approach. A cost function is the testing of statistical relationships between inputs (the independent variables) and cost (the dependent variable) using multiple regression techniques.
Input factors were selected from the results of the first component of this study.
The two primary purposes in selecting multiple regression for this study were: (1) to derive the best linear prediction equation from a large set of independent variables, and (2) to evaluate the respective contributions of a specific variable while holding other factors constant within a multivariate context.
Regression Analysis
The dependent measure was per diem cost. Seventeen independent variables were initially entered into the equation, including: (1) region, (2) metropolitan/non-metropolitan location, (3) profit/non-profit status, (4) family operation, (5) system membership, (6)
licensed capacity, (7) occupancy rate,
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September 30, 1981
Page 20
(8) size, (9) number of full-time employees in direct care, (10) proportion of severely or profoundly mentally retarded residents, (11) proportion of residents that needs to be completely fed, (12) proportion of non-ambulatory residents, (13) proportion of residents
with severe behavior problems, (14) proportion of residents who are not toilet trained, (15) average age of residents, (16) staff to resident ratio, and (17) years of operation.
Table 31 presents a correlation matrix of the predictors and per diem costs for
ICF-MRS. Staff to resident ratio was most highly correlated with per diem cost (r = .70, p <.01). In descending order of magnitude, per diem cost was correlated with the proportion of residents who were not toilet trained (r = .55, p < .01) and who need to be completely fed (r = .51,p < .01). Average age of residents was negatively correlated with per diem cost (r =-.46, p < .01).
The correlation ratios are in agreement with the analysis of variance results
reported earlier in this paper. Higher staff to resident ratios were associated with higher per diems. Higher proportions of non-toilet trained residents were associated with higher per
diems. Higher proportions of residents who had to be completely fed were associated
with higher per diems. An inverse relationship existed between per diem and average
age of residents.
It is obvious that there is some degree of correlation among the independent
variables. For example, facilities with higher proportions of non-ambulatory residents or those which serve children may require higher staff complements. All three of these variables are associated with higher per diem rates. The implications are that correlated variables "pick up" and reflect influences exerted by other variables thereby increasing their own apparent "causal" impact upon the dependent variable. The results become
mixed because of correlation; readers must, therefore, exercise caution in interpreting these findings and should not point to a single variable as ~ determinant of per diem variation.
The results of the multiple regression analysis for ICF-MRS suggest that eight variables were statistically significant determinants of per diem rates: (1) staff to resident ratio, (2) number of non-ambulatory residents, (3) years of operation of facility,
(4) average age of residents, (5) profit/non-profit status of facility, (6) facility size, (7) family owned and operated facilities, and (8) licensed capacity.
The overall multiple regression analysis accounted for 75 percent of the variance
in per diems (multiple R = .87). The eight statistically significant variables accounted for 73 percent of that variance and were significant at the p < .01 level.
These findings corroborate earlier work by O'Connor and Morris (1978) and Wieck and Bruininks (1980) who reported that factors reflecting dependency level of residents, staff to resident ratio, and age of residents are extremely intertwined with the services provided by the facility and concomitant costs.
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Table 31
Correlation Matrix of Predictors and Dependent Variable for ICF-MRS
Per Diem
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1. Region
.36
2. Metro/Non-Metro .37 .75
3. Profit/Non-Profit -.09 -.04 .06
4. Family Operated .28 .26 .19 -.60
5. Systems Member -.08 -.05 -.11 .15 -.50
6. Licensed Capacity -.01 .17 .15 .09 .00 .20
7. Occupancy Rate .00 .09 .15 .05 .16-.24-.04
8. Size -.02 .17 .15 .10 .01.19 1.0 -.01
9. HE Direct Care .38 .26 .24 -.09 .11 .18 .81 -.10 .80
10. Staff to Resident Ratio .70 .28 .31 -.31 .24 -.13 -.04 -.08 -.06 .39
11. Years of Operation -.19 -.2T -.13 .13 -.30 .20 .22 -.20 .22 .23 -.01
17. Average Age -.46 -.24 -.28 .05 -.24 .18 .05-.14 .06-.21-.40-.17-.22 -.32-.31 .32-.35
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V. SUMMARY OF FINDINGS
Location
There were significant differences (p < .01) in the per diems of ICF-MRS
located in Minnesota's eleven economic development regions. Mean rates ranged
from $31.50 and $31.84 in Regions 6 and 1 to $44.11 in Region 11. Regional
variations may be due to general cost-of-living differences, or to differences in the supply and demand of one or more factors of "production" (e.g., labor, capital, and materials).
ICF-MRS located in the seven-county, Minneapolis-Saint Paul metropolitan area
(Region 11) have significantly (p < .01) higher per diems than those in non-metropolitan areas. These differences may be attributable to cost of-living differences between urban and rural areas.
Size
A U-shaped relationship between size and per diem costs was found. Facilities
serving six or fewer residents and ICF-MRS serving 33 or more residents reported
the highest per diems ($41 .08 and $42.13, respectively). There was a significant
difference (p < .05) in per diems by size categories; the per diem differences between facilities serving seven to 12 persons ($35.55) and 13 to 16 residents ($36.66) and the other three sizes were especially significant (p< .01 for both). The question of economy of scale for residential services remains unresolved.
During 1979 there were approximately 3,470 persons living in Minnesota's 185
Intermediate Care Facilities for Mentally Retarded; the facilities ranged in size from six to 171. Seventy-five percent (N = 139) of the facilities were licensed to serve sixteen or fewer individuals; they served only 35.4 percent (N = 1,228) of the total resident population. The five largest facilities--averaging 123 residents--had a resident population of 616 persons. For further discussion of facility "size, " see Policy Analysis Series No. 2
(Developmental Disabilities Program, 1981 ). v. No significant differences were found between proprietary and non-profit facilities in the single variable analysis (refer to footnote #4, page 24 for multiple regression results). Family-owned and operated facilities reported significantly (p <.01) lower per diems ($34,22) than non-family owned and operated agencies ($41.00).
Systems
The results of this study indicate that systems of ICF-MRS operate at a significantly (p < .05) higher cost ($40.52) than ICF-MRS not affiliated with a system ($36.37). This result is similar to the findings of the national study by Wieck and Bruininks (1980).
Occupancy Rate
No statistically significant differences were reported in per diems based on
occupancy rates. ICF-MRS in Minnesota typically operate at a high
occupancy level.
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Number of Staff
A positive Pearson correlation coefficient (r = .39, p < .01) was reported between the number of FTE direct care staff and the per diem.
Staff-Resident Ratio
Statistically significant differences were reported for facilities based on
level of staff-resident ratio (p < .01). AS the staff-resident ratio increases,
the per diem also increases in a direct, positive relationship. Per diems ranged from $36.49 for facilities with a .33 staff-resident ratio or less to $64.92 for ICF-MRS with a staff-resident ratio of 1.33 or more.
Years of Operation
The highest per diems ($45.15) were reported by new facilities (two or less
years of operation) while the lowest per diems ($33.73) were reported by
ICF-MRS which were seven to 20 years old.
These differences were statistically significant (p < .01).
Class A or Class B
The analysis indicated that the difference between per diems for
Class B facilities ($54.55) and Class A facilities ($37.14) was
statistically significant (p < .01).
Proportion of Severely/Profoundly Mentally Retarded Residents
Facilities that served resident populations in which 40 to 49 percent were severely/ profoundly mentally retarded had lower per diems than facilities serving other proportions. Those differences were statistically significant (p< .01).
Resident Dependency
There was a positive, direct relationship between dependency level (feeding, ambulation, toilet training, behavior problems) and per diems. ICF-MRS that serve higher proportions of residents who must be completely fed, are non-ambulatory, are not toilet trained, or who have severe behavior problems report higher per diems. The differences in per diems for all of these facilities were statistically significant (p< .01).
Mean per diems by proportion of residents who are completely fed ranged from
$37.86 (zero to five percent) to $71.38 (40 percent or more); by proportion
of non-ambulatory residents, the range was $37.72 (zero to nine percent) to
$61.95 (20 to 39 percent). Per diems by proportion of non-toilet trained residents went from a low of $37.92 (zero to five percent) to a high of $59.47 (20 percent or more); for those facilities serving persons with severe behavior problems, per diems ranged from $36.78 (zero to nine percent) to $51.21 (20 percent or more).
Age of Residents
A statistically significant (p < .01) inverse relationship exists between
average resident age and per diem. ICF-MRS serving children reported the highest per diems ($51.16). Facilities for older populations (41 years or older) reported the lowest per
diems ($33.57). Facilities for teenagers (13 to 20 years) and younger adults (21 to 40 years) reported costs of $44.18 and $38.65, respectively.
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September 30, 1981
Page 24
Multiple Factors
When all of these factors are considered simultaneously, the variables producing
statistically significant variations in per diem rates were: (1) staff to resident
ratio, (2) proportion of residents who are non-ambulatory, (3) number f years in
operation, (4) age of residents, (5) profit/non-profit status, (6) facility size, (7) family owned and operated facilities, and (8) licensed capacity.
Correlation among variables makes all variables important, however, when
considering per diem rates in ICF-MRS and when determining policies relative to the
operation and regulation of intermediate care facilities for the mentally retarded.
VI. DISCUSSION
This study may have some significance really, aid the Welsch v. Noot Consent presented here and the issue of size must in terms of deinstitutionalization Decree specifically. The data pre however, be considered within a context broader than cost. Given this State's commitment to community placement of developmentally disabled persons and its often-stated policy of "establishing less restrictive, normalized living environments, the underlying concepts of deinstitutionalization must be considered as well:
Admissions to public residential facilities should be prevented by finding and developing alternative residential facilities;
All persons who have been prepared through programs of habilitation and training to function in appropriate community settings should be returned to community residential facilities;
Residential environments which protect human and civil rights and which contribute to the expeditious return of individuals to normal community living must be established and maintained. (National Association of Superintendents of Public Residential Facilities for the Mentally Retarded, 1974).
Within this context, it becomes important that policy-makers (and those making decisions about the allocation of public funds) become aware of all the costs of operating a community residential program--the psychosocial and developmental as well as the fiscal (Regional Institute of Social Welfare, 1976).
In a programmatic sense, decisions about facility size cannot be based solely upon
dollar costs. Although the literature is not definitive, research indicates that "smaller" community residences are more likely to provide environments which are more culturally normative and more influential in producing
4 The variable "profit/non-profit status" is significant in the multiple regression whereas it is not in the single variable analysis. When the variables are separated, as they are in the multiple regression, the correlation effects on "profit/non-profit" are reduced making the variable statistically relevant.
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September 30, 1981
Page 25
gains in adaptive behavior and general developmental growth. Various authors have
identified some factors which contribute to the psychosocial/developmental growth
of developmentally disabled residents (These factors are more often associated with
absences of security features, existence of personal effects, privacy in bathroom and bedroom areas (Balla, 1976; Baroff, 1980)
community exposure, social interaction (Crawford, 1979; Baroff, 1980)
experienced, trained direct care staff (Dellinger & Shope, 1978; Baroff, 1980)
The results from this study (again, the reader is advised that the data are from late 1979) indicate that per diem rates are higher for facilities serving six or fewer individuals;
lower for residences serving from seven to 12 persons and then increase again as the size of the facility exceeds 12 residents. Another study of group home costs in Minnesota (Department of Public Welfare, 1978) suggested that "smaller" facilities are capable of
producing "positive client changes at a better rate than larger ones; and...without significantly higher costs" (p. 75).
Cost is, of course, an important consideration--particularly during times of
economic instability. The data from this study suggest, however, that smaller residential facilities are not incompatible with cost considerations; nor are they inconsistent with State policy and the objectives specified in the Welsch v. Noot Consent Decree.
Many factors are involved in establishing and maintaining appropriate community
residences (Developmental Disabilities Program, 1981). And while costs are a very real and necessary consideration, they should not overshadow the individual needs of potential residents. As this study points out, there are a number of variables which influence the per
diem rates of ICF-MRs-many of those variables are directly or indirectly related to the characteristics of the persons living in those facilities.
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September 30, 1981
Page 26
REFERENCES/SOURCES
Audit Division. Computer tabulation of Rule 52 Cost Reports. Saint Paul, MN: Department
of Public Welfare, Audit Division, December 1979.
Balla, David A. Relationship of institutional size to quality of care: A review of the
literature. American Journal of Mental Deficiency, September 1976, 81 (2), 117-
124.
Baroff, George S. On "size" and the quality of residential care: A second look. Mental
Retardation, June 1980, 18 (3), 113-117.
Crawford, J., et al. Reinstitutionalization and community placement: Clinical
and environmental factors. Mental Retardation, July 1979, 17 (2), 59-63.
Dellinger, J. K., & Shope, L. J. Selected characteristics and working conditions of direct
service staff in Pennsylvania CLAS. Mental Retardation, February 1978, 16 (l),
19-21.
Developmental Disabilities Program. Policy Analysis Series #2: The Size of Community
Residential 'Facilities: Current Guidelines and Implications for of Energy, Planning
and Development, April 1981 (revised August 1981).
Division of Health Systems. Directory of licensed and certified health care facilities:
1980. Minneapolis, MN: Division of Health Systems. Department of Health,
March 15, 1980.
DPW Rule 52 Cost Reports (1979) on file in the Audit Division, Department of Public
Welfare, Saint Paul, Minnesota.
DPW Rule 52 (12 MCAR 2.052) Regulations for determining welfare per diem rates for
providers of residential services for the mentally retarded. (Revised January 1,
1977, and January 1, 1981).
ICF-MR facilities files: Licensing Division, Department of Public Welfare, Saint Paul,
Minnesota.
King, R. D., Raynes, N. V., & Tizard, J. Patterns of residential care: Sociological studies
in institutions for handicapped children. London: Routledge & Kegan Paul , Ltd.
McCormick, M., Balla, D., & Zigler, E. Resident care practices in institutions for retarded
persons: A cross-institutional, cross-cultural study. American Journal of Mental
Deficiency, July 1975, 80 (1), 1-17.
Minnesota Department of Public Welfare. The relationship of client capacity to client
development, client movement and costs in intermediate care facilities (ICF-MR) for
the mentally retarded: Final report (Karl W. Helner, Warren H. Bock, principal
investigators). Saint Paul, MN: Department of Public Welfare, _ MR Program
Division. September 1978.
Policy Analysis Paper #4
September 30, 1981
Page 27
National Association of Superintendents of Public Residential Facilities for the Mentally
Retarded. Contemporary issues in residential programming. Washington, D.C.:
President's Committee on Mental Retardation, 1974.
O'Connor, G., & Morris, L. A research approach to cost analysis and program budgeting
of community residential facilities. Eugene, OR: Rehabilitation Research and
Training Center in Mental Retardation, January 1978.
Peat, Marwick, Mitchell, & Co. The financial requirements of normalized residential
services and facilities for persons with developmental disabilities. Chicago: Illinois
Advisory Council on Developmental Disabilities, April 1976.
Piasecki, J., Pittinger, J., & Rutman, I. Determining the costs of community residential
services for the psychosocially disabled. Washington, D.C.: National Institute of
Mental Health, 1977.
Profile on MR residents in community residential facilities: fiscal year 1979 (Quality
Assurance and Review Program). Minnesota Department of Health, Minneapolis,
Minnesota.
Regional Institute of Social Welfare Research. Is statewide reinstitutionalization of
children's services a forward or backward social movement? Athens, GA:
University of Georgia, U.S. Department of Commerce, NTIS, 1976.
Welsch v. Noot, No. 4-72 Civ. 451 (D. Minn., filed Sept. 15, 1980).
Wieck, C. A. & Bruininks, R. H. The cost of public and
community residential care for mentally retarded people In the United States.
Minneapolis, MN: University of Minnesota, Department of Psychoeducational
Studies, 1980.
The Policy Analysis Series is published by the Minnesota Governor's Planning
Council on Developmental Disabilities and the Developmental Disabilities Program,
Department of Energy, Planning and Development.
Bruce Balow, Ph.D., Chair - Colleen Wieck, ph.D., Director
The purpose of this series is to enhance communication among state and
local agencies, service providers, advocates, and consumers on timely issues. We encourage reader participation by giving us feedback on your ideas and perceptions of this problem. The collection of data for this study was completed with the cooperation and kind assistance of Thomas Neumann, Audit Division, Minnesota Department of Public Welfare.
This paper may be cited: Developmental Disabilities Program.
Policy Analysis
Series #4: cost
Function Analysis of Minnesota Intermediate Care Facilities for Mentally Retarded
(ICF-MR) Per Diems. St. Paul, MN: Developmental Disabilities Program, Department of Energy, Planning and Development. September 30, 1981.
