Psychometric Modeling of Consumer Decisions in Primary Health Care By K.C. Koutsopoulos, R.J. Meyer, and D. Henley A psychometric technique, functional measurement, was used to measure the preferences of 77 persons for hypothetical health care providers identified by various levels of cost, travel time, and waiting time; responses were subjected to analysis of variance and graphic analysis to determine the functional relation by which respondents combined the three attributes in arriving at their preferences. Both modes of analysis suggested multiplicative decision models, but these yielded lower values of R2 than did linear models derived for comparison. Respondents were grouped by the proportion of response variance that was explained by each of the three attributes, and decision models were derived for each group. Discriminant analysis of socioeconomic characteristics of the respondents identified the variables that distinguished the groups and contributed to forming their preferences.
The health care delivery system in the United States faces problems that include maldistribution and shortage of physicians, inequities in accessibility and availability of health services, and lack of coordination between local and regional planning organizations [1]. Many research efforts have been directed toward understanding these imbalances and seeking ways to rectify them; one important finding is that consumers do not always seek health care even when they need it and facilities are available [2,3]. This finding suggests that the study of consumer decision making with respect to health care is a necessary step toward understanding some of the problems facing the health care delivery system. If we knew the processes by which such decisions are made we might be able to design a health care system such that consumer response and facility utilization would be optimized. Unfortunately, we are still far from attaining the goal of understanding consumer decision-making processes. A number of hypotheses have been suggested concerning causeeffect relationships in demand for health care [2,4], and information has been gathered on attitudinal measures of health care-related behavior [5-8] and the functional relation of such measures to demand for care [2,9], but few behavioral or cause-effect postulates have been firmly established. A primary obstacle to making causal inferences in health services from the National WINTER Address communications and requests for reprints to K.C. Koutsopoulos, Assis- WITE tant Professor, Department of Geography, University of Iowa, Iowa City, IA 52242. R.J. Meyer and D. Henley are doctoral candidates in the Department of Geography, 427 This research was supported by grant no. 5507RR07035-11
Institutes of Health. University of Iowa.
KOUTSOPOULOS, MEYER & HENLEY
research is the difficulty of imposing experimental control on social systems. Research on the effect of distance on health care-seeking behavior, for example, would be greatly facilitated if it were possible to manipulate the locations of providers while holding all other attributes of the system (e.g., quality of service) constant. Such manipulations are dearly not feasible, and, as a result, presently available data on health care behavior are generally correlational in nature. Consequently, existing models of consumer demand (e.g., refs. 2 and 5) are largely descriptive and do not provide a basis for the establishment of causal "laws" that might be used in prediction. Attitudinal modeling based on measurement of consumer preferences avoids the impossible requirement of experimental control of the social system and affords a means of approaching such cause-effect relationships through the study of decision making in a laboratory environment. The two principal methods of preference measurement are conjoint trade-off analysis [10-13] and functional measurement [14]. The two approaches differ in terms of their assumptions about response data: in functional measurement, subjective preference ratings are assumed to provide an interval-scale measure, whereas in conjoint analysis, responses are assumed to be merely ordinal rankings of preference. A more detailed discussion of metric versus nonmetric methods has been provided by Anderson [15]. Functional measurement offers a number of important advantages despite its assumptive drawbacks. Specifically, it is possible to estimate models of decision making at the individual level, rather than only for groups as with conjoint analysis, and it is possible to derive the functional form of the model that best describes how stimulus attributes were combined in the formation of overall preferences. This article describes an application of this method to the study of consumers' decisions about primary health care and examines variations in decision making among individuals in terms of their socioeconomic backgrounds. The investigation was exploratory, and no inferences are offered about the general nature of health care decisions. The prime concern was to assess the usefulness and applicability of this method in a health care context.
Functional Measurement
HEALTH SERVICES
RESEARCH
428
Functional measurement evolved from the view that persons are information processors. That is, when a person forms a judgmentabout anything from the goodness of a health care facility to the likeability of another person-he or she cognitively combines perceptions of a set of attributes of the judged entity to arrive at an overall evaluation. Each attribute is assumed to be describable in terms of its subjective scale value (perceived magnitude) and its weight (relative importance in the decision-making task). The theory also posits that the various attributes are combined according to an implicit rule that can be described mathematically. For example, a person's overall response ri can be expressed as
=
gi(w8, Sa)
where w. are weights and sa are subjective scale values of the attributes under consideration; the function gi is most commonly the sum or the product. Application of the method typically involves presenting, in a factorial design, descriptions of hypothetical entities (providers) expressed in terms of different levels of attributes (such as location, cost, and waiting time); the subjects rate, on a line scale, the desirability of all possible combinations of the different values of the attributes. The factorial design enables the researcher to test for the appropriate combination rule, the form of the function gi, through an analysis of variance of the response data. The subjective scale values usually correspond to marginal means across rows or columns of the factorial matrix, and weights may be derived either directly through examination of main effects (if the combination rule is linear) or through numerical estimation (if it is nonlinear). Anderson [15] has discussed the technique in detail. The literature on applications of the technique includes studies of such judgment tasks as mass transit evaluation [161, supermarket preference [17], formation of personality impressions [18], and clinical decisions [19]. Although most of these studies have been exploratory in nature they have helped establish the utility of the approach in different contexts. The results of these studies argue against traditional regression approaches to modeling consumer preferences. Unlike regression, the functional measurement method does not require an assumption about the form of the combining function; on the contrary, it permits one to derive that form, which provides an empirical basis for estimating responses to changed values of system attributes.
MODELING HEALTH CARE DECISIONS
a
Methods A four-part questionnaire was administered to 77 people in a random sample of residents of Cedar County, Iowa. The first part of the questionnaire measured the respondents' preferences for a set of hypothetical health care providers; the second part was a series of questions about need for and perception of health care services; the third part induded questions on the respondents' current use of health care; and the fourth part elicited socioeconomic and demographic information on the respondents and their families. The functional measurement part of the survey instrument had a 33 factorial design in which the stimuli were all possible combinations of three levels of each of three provider characteristics: cost per visit (C1 = $3, C2 = $7, and C3 = $11), travel time (T1 = 10 min, T2 = 25 min, and Ts =40 min), and waiting time (W1 = 15 min, W2 = 45 min, and Ws = 90 min). These characteristics were selected on the basis of the health services literature; a pilot study before the survey indicated that they were frequently listed as the most important attributes of primary health care providers, and, among the numerous characteristics that could be selected, this set seemed most directly controllable
WINTER 1977
429
KOUTSOPOULOS, by planning or government agencies. The levels of each characteristic MEYER & dosely resembled the actual range of values in the study area. HENLEY A typical stimulus combination was arranged as follows: The travel time to the provider is 10 minutes. The cost per visit is $7. The waiting time is 45 minutes. Would never go I Would always go The line scale assocated with each stimulus was assigned a numerical range from 0 (would never go) to 20 (would always go), and each subject was asked to indicate his rating of a stimulus by marking the line with a slash. Each subject practiced on several preliminary questions until he felt confident that he understood the rating task; then the 27 experimental stimuli were presented (twice in random sequence for each stimulus) for his responses. The test and interview were conducted for each subject individually. The whole procedure required about 30 minutes per subject, and each subject was paid $3 for his cooperation.
Analysis The survey results were subjected to analyses of variance to determine the appropriate combining function: the significance of the variance explained by the attributes and their interactions was determined by examination of the F-ratios; then interaction graphs were plotted of the mean responses to sets of stimuli in which only one of the three attributes varied. For example, the three stimuli involving C1 and T1 can be represented by C1T1W1, C1T1W2, and C1T1Wg; a response (to the last, say) is denoted (C1T1W8). The mean of all responses to the three stimuli is (CLT1W), and this value was plotted, together with (C1T2W) and (C1T8W), on axes showing response value and values of T. Thus a curve was generated for the mean change of preference for travel time across all values of waiting time, with cost held constant. Similar curves for (C2T1W), (C2T2W), and (C2T8W) showed the mean change with cost constant at C2, and so on. The same procedure was followed for all such sets of stimuli; the slopes and the degree of convergence/divergence or parallelism of the three lines for the three levels of the constant attribute offer explicit geometric evidence as to whether the relation between C, T, and W is additive or multiplicative [20].
Results The results of the analysis of variance in the whole sample are shown in Table 1. Each of the two-way interactions was significant, which suggests that a multiplicative model might be an appropriate HEALTH decision model at the group level. Analyses of variance for individual REEARCES subjects (based on the two response sets for each subject) indicated, however, that the two-way and three-way interactions for individuals 430 were not all significant: some respondents may have made their deci-
Table 1. Analysis of Variance in Preference Responses of Whole Sample
MODELING
HEALTH CARE
DECISIONS
Sums of Mean d.f. FF squares square W .................... 27 182.35035 2 13591.17518 231.51* T .................... 6 398.38188 2 3 199.19094 121.97* C ..................... 14 390.09960 2 7 195.04980 166.88* WXT ................ 331.58058 4 8289515 5.970 W x C............ 4 610.34935 152.58734 14.27 TXC ................ 347.49349 4 86.87337 7.98 WXTXC ............ 65.37287 8 8.17161 1.30 Error between ......... 28 203.05556 146 193.17161 ... Error in W ........... 17 142.33033 292 58.70661 ... Error in T ........... 7 658.93093 292 26.2M922 ... Error in C ............ 12589.66667 292 43.11530 ... Error in W X T ....... 8113.04805 584 13.89221 ... Error in WXC . 6243.71772 584 10.69130 Error in TX C ....... 6 359.63964 584 10.88979 ... Error in WX TX C ... 7334.65165 1168 6.27967 Tota ................. 143 443.05380 3995 * Significant at p < 0.001. Source
...
sions on the basis of a linear model. It is possible, however, that the nonsignificance of these interactions might be due to the low power of individual significance tests-with only two response sets, individual interaction terms were tested with only one and eight degrees of freedom. The interaction terms for the entire sample were examined further in the interaction graphs, including those shown in Fig. 1. These graphs reveal a general tendency for responses to converge in the presence of an undesirable level of a particular factor, as would be expected from a multiplicative relation among the attributes. Thus the form r= WaCbTc+e
appears to be an appropriate model of the responses.
Grouping Decision Makers The analyses of variance in the responses of individuals were examined to determine whether the sample could be divided into groups of similar decision makers. The grouping criterion was the amount of importance individuals ascribed to each factor, as revealed by the proportion of variance explained by each factor in the individual analyses of variance. Variance proportions explained by travel time, waiting time, and cost for the 77 respondents were subjected to the euclidian-distance WINTER grouping algorithm of Ward [21]. In this procedure, pairs of similar 1977 observations are sequentially replaced by one centroid until all observations are described by a single centroid. If the data set comprises a 431
KOUTSOPOULOS, MEYER & HENLEY
Fig. 1. Mean spe rsponses to waiting time at three levels of cost (C) over all travel times (left), to waiting time at three levels of travel time (T) over all costs (center), and to travel time at three levels of cost over all waiting times. 20-
C
c
0
C 10-
T_
$3 $7 -$11
0
Co0.
it 0
I
15
$3 $7 $11
10 25
1
90 45 Waiting time
15
45
Waiting time
90
10
25 40 Travel time
salient set of clusters, the iteration at which the process is stopped is generally the step before a quantum jump in information loss [211. That step or iteration is determined by plotting the amount of detail lost against the number of iterations; the optimal grouping is that produced by the step preceding an abrupt change in the curve. In this study the optimal grouping occurred at the 73rd iteration. Four groups appeared: group W, the waiting time group, included 28 sample members who considered waiting time almost exclusively; group C, the cost group, comprised 11 who considered mainly cost; group T, the travel time group, consisted of nine persons who considered mainly travel time; and group WC, the waiting time and cost group, contained 29 sample members who considered waiting time and cost more or less equally but disregarded travel time. In the 74th iteration, members of group WC were reassigned to the single-factor groups W and C, yielding three groups. No statistical criterion exists for the optimal solution in grouping analyses, so both these results were retained for consideration in a discriminant analysis using socioeconomic data, discussed later. Responses of each of the four initial groups were subjected to analyses of variance to derive group decision models for comparison. Graphs of all the two-way interactions were also examined. These analyses suggested that a multiplicative model might be an appropriate combination rule for all groups. Although all of the graphs exhibited the convergence characteistic of a multiplicative model, they differed in slope and spacing of the response lines, reflecting differences in weights and scale values among the groups. For example, in the mean HEALTH waiting time-cost interactions over all travel times (Fig. 2), it can be SERVICES seen that group W generated quite steep slopes (high responsiveness to RESEARCH waiting time) and narrow spacing (little responsiveness to cost). This pattern is very much in contrast to that of group C, which generated
432
Fig. 2. Mean responses of groups W, C, and WC to waiting time at three levels of cost over all travel times. 20
a.
Group W 15
45
$3~~~~~~~~$ $3 $7 $11 90
~~~~~~~~~~11
$13
Group C 15 45 Waiting time
MODELING DECISIONS
GroupWC 90
15
45
90
flat slopes (little responsiveness to waiting time) and wide spacing between cost levels (high responsiveness to cost), and that of group WC, which generated relatively steep slopes and wide spacing, indicating responsiveness to both waiting time and cost. (The graphs in Fig. 1, representing the entire sample, reveal nonzero slopes and moderately wide spacing, indicating that all three factors had some importance in the aggregate results.) The rest of the interaction graphs are not shown; however, the differences in slope and spacing generated by the four groups strongly supported the results of the grouping algorithm.
Fitting Models On the basis of these results, a multiplicative model for the entire sample and each of the four initial eudidian-distance groups was estimated by means of a least-squares regression on a log transformation of the variables. For comparative purposes, a linear model was also fit. The resulting models and the proportions of variance they explained are as follows: For the whole sample (N = 77): r = WO-600 T0P705 CO482 + e r = -0.53W - 0.35T - 0.75C + e For group W (N = 28): r = W0.419 T0 794 C08" + e r = -0.94W - 0.26T - 0.18C + e For group T (N = 9): r O= W61 T0O487 C0.75 + e r =-0.52W - 0.77T - 0.29C + e For group C (N= l1): WO.44 TO.819 C09402+ e r W= r =-0.19W - 0.22T - 0.95C + e For group WC (N = 29): r = WO.69 To.748 CO.527 + e r = -0.62W - 0.28T - 0.66C + e
R2= 0.906 R2 = 0.966 R2 = 0.840 R2 = 0.978 R2 = 0.843
R2= 0.949
R2=0.891 R2 = 0.984
R2=0.854 R2 = 0.900
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1977 433
KOUTSOPOULOS, MEYER & HENLEY
The coefficients of the linear model for the sample suggest cost as the most important factor in the aggregate decision, with waiting time and travel time of successively less importance. The group models, however, indicate that the aggregate model does not reflect the way decisions were actually made: the sample consisted of a set of quite discrete groups of decision makers, and no group model much resembles another or the aggregate model. All of the linear models provided higher values of R2 than did the multiplicative ones, despite the evidence from the interaction graphs for the latter as "correct." This apparent predictive failure of the multiplicative models is of primary methodological interest. Such a finding is not unique and was the subject of an article by Birnbaum [22], who indicated that an incorrect (poorly fitting) model sometimes provides better predictions of data than does a model that fits existing data better. Birnbaum showed that even when the data are perfectly multiplicative, comparison of correlation coefficients can lead to the erroneous conclusion that the linear model provides the better representation. Correlation coefficients can therefore be inappropriate for comparing additive and multiplicative models, because "the source of this difficulty lies in the assumption, implicit in the use of [the additive form], that the a priori values of [the variables] are positive and known to be on a ratio scale" [22]. Functional measurement, however, requires neither a priori values for the stimuli nor ratio scales for the responses. As a result of these and other advantages [14] of functional measurement over the correlational approach, it can be argued that if decision making is accurately captured by the measurement process, the model derived from interaction plots of the responses will predict better than any other.
Socioeconomic Characteristics of the Groups Data on socioeconomic characteristics and the actual health care utilization of the respondents were analyzed to see if such measures could serve as discriminants among the groups. Both sets of groups resulting from the euclidian-distance grouping algorithm were subjected to pairwise multiple discriminant analyses, using several sets of discriminating variables. Results from the two sets of groups were similar, although analysis of the three-group set was slightly more successful; thus only the result for the three groups "wait" (N = 41), "travel" (N = 9), and "cost" (N = 27) are presented. Discrimination was dearest between the "wait" and "travel" groups. A 13-variable model correctly assigned all 50 members; the variables that discriminated best were car availability (the "travel" group tended to have less access to an automobile), children (the "wait" group tended to have more of them), and current use of health care (the "travel" group tended to seek health care more often). A 12-variable model HEALTH correctly assigned 59 out of 68 members of the "wait" and "cost" SERVICES groups. These groups differed principally in car availability (the RESEARCH "cost" group had less access), age (the "cost" group tended to be older), 434 and current use of health care (the "cost" group sought care more
MODELING Table 2. Mean Responses of Three Groups on Socioeconomic and HEALTH DECISIONSCARE
Care-utilization Variables
Group Wait Cost (N = 41) (N= 27)
Variable
Age
...........................................
Sex (male=1, female=0) ........................... Years of education completed ...................... Houshold income per capita* ..................... Total children in household (younger than 18 and unemployed) ............ No. of preschool children in houshold. ........... dence in county ....................... Years of Full-time employment (yes=l, no=O). ............. Driver's licene (yes =1, no =) .................... Car availability (subjective scale
rating: "never" = 0, "always" = 20)
44.26
Travel (N = 9)
52.19 0.23 12.00 2.00
49.25 0.25 13.12 2.12
1.04 0.42 32.65 4..7 0.27 0.88 0.95
1.00 0 36.00 0.38 0.75
0.21 13.14 2.60 1.63 035 28A7
..............
19.37
17.31
14.12
No. of health care visits per year by all household members ...................... Per-visit cost of usual provider, $ ................... Distance to usual provder, miles .................. Usual time between making appointment
2.60 9.44 7.40
4.46 7.96 9.15
3.25 5.88 3.00
and seeing provider, days ..................... 4.28 Waiting time in usual provider's office, min ........ 26.65 More frequent care desired (yes=l, noO=0) ......... 0.19
1.23 32.38
1.88 23.12 0.62
0.19 Special health problem in household requing care more often than usual (yes= 1, no =0) 0.25 0.42 0.27 * Scored on categories: less than $3,000 = 1; $3,000-5,999 = 2; $6,000-8,999 = 3; $9,000-11,999 = 4; $12,000-14,999 = 5; $15,000-24,999 = 6; more than $25,000 = 7. .....
often). A seven-variable model correctly assigned 28 out of 36 members of the "travel" and "cost" groups. The chief discriminants were car availability (the "cost" group had greater access), children (the "cost" group had more children), whether respondents would seek more health care if they could (the "cost" group would seek more care), education (the "cost" group tended to have less), and income (the "cost" group tended to earn less). Group differences were also reflected in the means of the variables for each group, shown in Table 2. The "wait" group was younger, had more income, was more fully employed, had more children, and had come more recently to Cedar County. In contrast, the "cost" group was older and had less income. The "travel" group was composed of persons who lived dose to the health care provider they usually patronized and had less access to an automobile.
Discussion
The extent to which planning is successful in achieving uniform utilization of health services depends on its ability to adjust service delivery to accommodate consumer decision making. The methods illustrated in this artidle provide an approach to the study of consumer preference that can help clarify the adjustments needed. Modeling the formation of individual preferences for primary health care providers
1977TER 435
KOUTSOPOULOS, MEYER & HENLEY
offers a potentially useful tool for understanding the trade-offs among provider attributes on which consumer decisions are based. Further, the results suggest that differences in decision making, as measured in an experimental setting, are related to respondents' socioeconomic and behavioral characteristics. With further study it should be possible to predict the decision-making strategies of large populations on the basis of surveys of relatively small samples. Health care decisions are different in many respects from those treated in most consumer research: hence one would not expect an easy transfer of methods from one context to another. This research has illustrated some of the possibilities of the transfer of psychometric modeling techniques to the study of consumer health care decisions. Despite the many problems remaining unsolved, the results are promising and encourage further work in this direction.
REFERENCES 1. Barnhart, G. Social design and operations research. Public Health Rep 85:247 Mar. 1970. 2. Andersen, R. A Behavioral Model of Families' Use of Health Services. Research Series 25, Center for Health Administration Studies, University of Chicago, 1968. 3. Hetherington, R.W. and C.E. Hopkins. Symptom sensitivity: Its social and cultural correlates. Health Serv Res 4:63 Spring 1969. 4. Wirick, G. A multiple equation model of demand for health care. Health Serv Res 1:301 Winter 1966. 5. Steele, J.L. Conceptual and empirical dimensions of health behavior. J Health Soc Behav 13:382 Dec. 1972. 6. Brooks, C.H. Associations among distance, patient satisfaction and utilization of two types of inner-city dinics. Med Care 11:62 Sept.-Oct. 1973. 7. Monteiro, LA. Expense is no object: Income and physician visits reconsidered. J Health Soc Behav 14:99 June 1973. 8. Colburn, D. and C.R. Pope. Socioeconomic status and preventive health behavior. J Health Soc Behav 15:67 June 1974. 9. Aday, L.A. and R. Andersen. A famework for the study of access to medical care. Health Serv Res 9:208 Fall 1974. 10. Luce, RD. and J.W. Tukey. Simultaneous conjoint measurement: A new type of fundamental measurement. J Math Psychol 1:1 Feb. 1964. 11. Krantz, D.H. and A. Tversky. Conjoint-measurement analysis of composition rules in psychology. Psychol Rev 78:151 Mar. 1971. 12. Acto, F. Consumer Preferences for Health Care Services: An Exploratory Investigation. Doctoral dissertation, Department of Hospital and Health Administration, State University of New York at Buffalo, 1976. 13. Wind, Y. and L.K. Spitz. Analytical approach to marketing decisions in healthcare organizations. Oper Res 24:973 Oct. 1976. 14. Anderson, N.H. Functional measurement and psychological judgment. Psychol Rev 77:152 May 1970. 15. Anderson, N.H. Information Integration Theory: A Brief Survey. In D.H. Krantz, R.C. Arkinson, R.C. Luce, and P. Suppes (eds.), Contemporary Development in Mathematical Psychology, Vol. 2, pp. 236-305. San Francisco: Freeman,
1974.
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16. Koutsopoulos, K.C. and R.J. Meyer. Mass Transit Decision Making Market Segmentation: A Pilot Study. Technical Report No. 69, Institute of Urban and Regional Research, University of Iowa, 1976. 17. Louviere, J.J. and R.J. Meyer. Modeling consumer response to alternative shopping opportunities: A behavioral approach. Paper presented at the 1974 Annual Meeting of the West lakes Association of American Geographers, Atlanta, GA, Oct. 1974. 18. Anderson, N.H. Basic Experiments in Person Perception. Technical Report No. 43, Center for Human Information Processing, University of California at San Diego, 1974.
19. Anderson, N.H. Looking for configurality in dinical judgment. Psychol Bull. 78:93 Aug. 1972. 20. Koutsopoulos, K.C. Modeling Public Response to Rural Health Care Providers. Technical Report, Institute of Urban and Regional Research, Univenity of Iowa (forthcoming). 21. Ward, J.H. Hierarchical grouping to optimize an objective function. J Am Stat Assoc 58:236 Mar. 1963. 22. Bimbaum, MaH The devil rides again: Correlation as an index of fit. Psychol Bull 79:239 Apr. 1973.
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The health care delivery system in the United States faces problems that include maldistribution and shortage of physicians, inequities in accessibility and availability of health services, and lack of coordination between local and regional planning organizations [1]. Many research efforts have been directed toward understanding these imbalances and seeking ways to rectify them; one important finding is that consumers do not always seek health care even when they need it and facilities are available [2,3]. This finding suggests that the study of consumer decision making with respect to health care is a necessary step toward understanding some of the problems facing the health care delivery system. If we knew the processes by which such decisions are made we might be able to design a health care system such that consumer response and facility utilization would be optimized. Unfortunately, we are still far from attaining the goal of understanding consumer decision-making processes. A number of hypotheses have been suggested concerning causeeffect relationships in demand for health care [2,4], and information has been gathered on attitudinal measures of health care-related behavior [5-8] and the functional relation of such measures to demand for care [2,9], but few behavioral or cause-effect postulates have been firmly established. A primary obstacle to making causal inferences in health services from the National WINTER Address communications and requests for reprints to K.C. Koutsopoulos, Assis- WITE tant Professor, Department of Geography, University of Iowa, Iowa City, IA 52242. R.J. Meyer and D. Henley are doctoral candidates in the Department of Geography, 427 This research was supported by grant no. 5507RR07035-11
Institutes of Health. University of Iowa.
KOUTSOPOULOS, MEYER & HENLEY
research is the difficulty of imposing experimental control on social systems. Research on the effect of distance on health care-seeking behavior, for example, would be greatly facilitated if it were possible to manipulate the locations of providers while holding all other attributes of the system (e.g., quality of service) constant. Such manipulations are dearly not feasible, and, as a result, presently available data on health care behavior are generally correlational in nature. Consequently, existing models of consumer demand (e.g., refs. 2 and 5) are largely descriptive and do not provide a basis for the establishment of causal "laws" that might be used in prediction. Attitudinal modeling based on measurement of consumer preferences avoids the impossible requirement of experimental control of the social system and affords a means of approaching such cause-effect relationships through the study of decision making in a laboratory environment. The two principal methods of preference measurement are conjoint trade-off analysis [10-13] and functional measurement [14]. The two approaches differ in terms of their assumptions about response data: in functional measurement, subjective preference ratings are assumed to provide an interval-scale measure, whereas in conjoint analysis, responses are assumed to be merely ordinal rankings of preference. A more detailed discussion of metric versus nonmetric methods has been provided by Anderson [15]. Functional measurement offers a number of important advantages despite its assumptive drawbacks. Specifically, it is possible to estimate models of decision making at the individual level, rather than only for groups as with conjoint analysis, and it is possible to derive the functional form of the model that best describes how stimulus attributes were combined in the formation of overall preferences. This article describes an application of this method to the study of consumers' decisions about primary health care and examines variations in decision making among individuals in terms of their socioeconomic backgrounds. The investigation was exploratory, and no inferences are offered about the general nature of health care decisions. The prime concern was to assess the usefulness and applicability of this method in a health care context.
Functional Measurement
HEALTH SERVICES
RESEARCH
428
Functional measurement evolved from the view that persons are information processors. That is, when a person forms a judgmentabout anything from the goodness of a health care facility to the likeability of another person-he or she cognitively combines perceptions of a set of attributes of the judged entity to arrive at an overall evaluation. Each attribute is assumed to be describable in terms of its subjective scale value (perceived magnitude) and its weight (relative importance in the decision-making task). The theory also posits that the various attributes are combined according to an implicit rule that can be described mathematically. For example, a person's overall response ri can be expressed as
=
gi(w8, Sa)
where w. are weights and sa are subjective scale values of the attributes under consideration; the function gi is most commonly the sum or the product. Application of the method typically involves presenting, in a factorial design, descriptions of hypothetical entities (providers) expressed in terms of different levels of attributes (such as location, cost, and waiting time); the subjects rate, on a line scale, the desirability of all possible combinations of the different values of the attributes. The factorial design enables the researcher to test for the appropriate combination rule, the form of the function gi, through an analysis of variance of the response data. The subjective scale values usually correspond to marginal means across rows or columns of the factorial matrix, and weights may be derived either directly through examination of main effects (if the combination rule is linear) or through numerical estimation (if it is nonlinear). Anderson [15] has discussed the technique in detail. The literature on applications of the technique includes studies of such judgment tasks as mass transit evaluation [161, supermarket preference [17], formation of personality impressions [18], and clinical decisions [19]. Although most of these studies have been exploratory in nature they have helped establish the utility of the approach in different contexts. The results of these studies argue against traditional regression approaches to modeling consumer preferences. Unlike regression, the functional measurement method does not require an assumption about the form of the combining function; on the contrary, it permits one to derive that form, which provides an empirical basis for estimating responses to changed values of system attributes.
MODELING HEALTH CARE DECISIONS
a
Methods A four-part questionnaire was administered to 77 people in a random sample of residents of Cedar County, Iowa. The first part of the questionnaire measured the respondents' preferences for a set of hypothetical health care providers; the second part was a series of questions about need for and perception of health care services; the third part induded questions on the respondents' current use of health care; and the fourth part elicited socioeconomic and demographic information on the respondents and their families. The functional measurement part of the survey instrument had a 33 factorial design in which the stimuli were all possible combinations of three levels of each of three provider characteristics: cost per visit (C1 = $3, C2 = $7, and C3 = $11), travel time (T1 = 10 min, T2 = 25 min, and Ts =40 min), and waiting time (W1 = 15 min, W2 = 45 min, and Ws = 90 min). These characteristics were selected on the basis of the health services literature; a pilot study before the survey indicated that they were frequently listed as the most important attributes of primary health care providers, and, among the numerous characteristics that could be selected, this set seemed most directly controllable
WINTER 1977
429
KOUTSOPOULOS, by planning or government agencies. The levels of each characteristic MEYER & dosely resembled the actual range of values in the study area. HENLEY A typical stimulus combination was arranged as follows: The travel time to the provider is 10 minutes. The cost per visit is $7. The waiting time is 45 minutes. Would never go I Would always go The line scale assocated with each stimulus was assigned a numerical range from 0 (would never go) to 20 (would always go), and each subject was asked to indicate his rating of a stimulus by marking the line with a slash. Each subject practiced on several preliminary questions until he felt confident that he understood the rating task; then the 27 experimental stimuli were presented (twice in random sequence for each stimulus) for his responses. The test and interview were conducted for each subject individually. The whole procedure required about 30 minutes per subject, and each subject was paid $3 for his cooperation.
Analysis The survey results were subjected to analyses of variance to determine the appropriate combining function: the significance of the variance explained by the attributes and their interactions was determined by examination of the F-ratios; then interaction graphs were plotted of the mean responses to sets of stimuli in which only one of the three attributes varied. For example, the three stimuli involving C1 and T1 can be represented by C1T1W1, C1T1W2, and C1T1Wg; a response (to the last, say) is denoted (C1T1W8). The mean of all responses to the three stimuli is (CLT1W), and this value was plotted, together with (C1T2W) and (C1T8W), on axes showing response value and values of T. Thus a curve was generated for the mean change of preference for travel time across all values of waiting time, with cost held constant. Similar curves for (C2T1W), (C2T2W), and (C2T8W) showed the mean change with cost constant at C2, and so on. The same procedure was followed for all such sets of stimuli; the slopes and the degree of convergence/divergence or parallelism of the three lines for the three levels of the constant attribute offer explicit geometric evidence as to whether the relation between C, T, and W is additive or multiplicative [20].
Results The results of the analysis of variance in the whole sample are shown in Table 1. Each of the two-way interactions was significant, which suggests that a multiplicative model might be an appropriate HEALTH decision model at the group level. Analyses of variance for individual REEARCES subjects (based on the two response sets for each subject) indicated, however, that the two-way and three-way interactions for individuals 430 were not all significant: some respondents may have made their deci-
Table 1. Analysis of Variance in Preference Responses of Whole Sample
MODELING
HEALTH CARE
DECISIONS
Sums of Mean d.f. FF squares square W .................... 27 182.35035 2 13591.17518 231.51* T .................... 6 398.38188 2 3 199.19094 121.97* C ..................... 14 390.09960 2 7 195.04980 166.88* WXT ................ 331.58058 4 8289515 5.970 W x C............ 4 610.34935 152.58734 14.27 TXC ................ 347.49349 4 86.87337 7.98 WXTXC ............ 65.37287 8 8.17161 1.30 Error between ......... 28 203.05556 146 193.17161 ... Error in W ........... 17 142.33033 292 58.70661 ... Error in T ........... 7 658.93093 292 26.2M922 ... Error in C ............ 12589.66667 292 43.11530 ... Error in W X T ....... 8113.04805 584 13.89221 ... Error in WXC . 6243.71772 584 10.69130 Error in TX C ....... 6 359.63964 584 10.88979 ... Error in WX TX C ... 7334.65165 1168 6.27967 Tota ................. 143 443.05380 3995 * Significant at p < 0.001. Source
...
sions on the basis of a linear model. It is possible, however, that the nonsignificance of these interactions might be due to the low power of individual significance tests-with only two response sets, individual interaction terms were tested with only one and eight degrees of freedom. The interaction terms for the entire sample were examined further in the interaction graphs, including those shown in Fig. 1. These graphs reveal a general tendency for responses to converge in the presence of an undesirable level of a particular factor, as would be expected from a multiplicative relation among the attributes. Thus the form r= WaCbTc+e
appears to be an appropriate model of the responses.
Grouping Decision Makers The analyses of variance in the responses of individuals were examined to determine whether the sample could be divided into groups of similar decision makers. The grouping criterion was the amount of importance individuals ascribed to each factor, as revealed by the proportion of variance explained by each factor in the individual analyses of variance. Variance proportions explained by travel time, waiting time, and cost for the 77 respondents were subjected to the euclidian-distance WINTER grouping algorithm of Ward [21]. In this procedure, pairs of similar 1977 observations are sequentially replaced by one centroid until all observations are described by a single centroid. If the data set comprises a 431
KOUTSOPOULOS, MEYER & HENLEY
Fig. 1. Mean spe rsponses to waiting time at three levels of cost (C) over all travel times (left), to waiting time at three levels of travel time (T) over all costs (center), and to travel time at three levels of cost over all waiting times. 20-
C
c
0
C 10-
T_
$3 $7 -$11
0
Co0.
it 0
I
15
$3 $7 $11
10 25
1
90 45 Waiting time
15
45
Waiting time
90
10
25 40 Travel time
salient set of clusters, the iteration at which the process is stopped is generally the step before a quantum jump in information loss [211. That step or iteration is determined by plotting the amount of detail lost against the number of iterations; the optimal grouping is that produced by the step preceding an abrupt change in the curve. In this study the optimal grouping occurred at the 73rd iteration. Four groups appeared: group W, the waiting time group, included 28 sample members who considered waiting time almost exclusively; group C, the cost group, comprised 11 who considered mainly cost; group T, the travel time group, consisted of nine persons who considered mainly travel time; and group WC, the waiting time and cost group, contained 29 sample members who considered waiting time and cost more or less equally but disregarded travel time. In the 74th iteration, members of group WC were reassigned to the single-factor groups W and C, yielding three groups. No statistical criterion exists for the optimal solution in grouping analyses, so both these results were retained for consideration in a discriminant analysis using socioeconomic data, discussed later. Responses of each of the four initial groups were subjected to analyses of variance to derive group decision models for comparison. Graphs of all the two-way interactions were also examined. These analyses suggested that a multiplicative model might be an appropriate combination rule for all groups. Although all of the graphs exhibited the convergence characteistic of a multiplicative model, they differed in slope and spacing of the response lines, reflecting differences in weights and scale values among the groups. For example, in the mean HEALTH waiting time-cost interactions over all travel times (Fig. 2), it can be SERVICES seen that group W generated quite steep slopes (high responsiveness to RESEARCH waiting time) and narrow spacing (little responsiveness to cost). This pattern is very much in contrast to that of group C, which generated
432
Fig. 2. Mean responses of groups W, C, and WC to waiting time at three levels of cost over all travel times. 20
a.
Group W 15
45
$3~~~~~~~~$ $3 $7 $11 90
~~~~~~~~~~11
$13
Group C 15 45 Waiting time
MODELING DECISIONS
GroupWC 90
15
45
90
flat slopes (little responsiveness to waiting time) and wide spacing between cost levels (high responsiveness to cost), and that of group WC, which generated relatively steep slopes and wide spacing, indicating responsiveness to both waiting time and cost. (The graphs in Fig. 1, representing the entire sample, reveal nonzero slopes and moderately wide spacing, indicating that all three factors had some importance in the aggregate results.) The rest of the interaction graphs are not shown; however, the differences in slope and spacing generated by the four groups strongly supported the results of the grouping algorithm.
Fitting Models On the basis of these results, a multiplicative model for the entire sample and each of the four initial eudidian-distance groups was estimated by means of a least-squares regression on a log transformation of the variables. For comparative purposes, a linear model was also fit. The resulting models and the proportions of variance they explained are as follows: For the whole sample (N = 77): r = WO-600 T0P705 CO482 + e r = -0.53W - 0.35T - 0.75C + e For group W (N = 28): r = W0.419 T0 794 C08" + e r = -0.94W - 0.26T - 0.18C + e For group T (N = 9): r O= W61 T0O487 C0.75 + e r =-0.52W - 0.77T - 0.29C + e For group C (N= l1): WO.44 TO.819 C09402+ e r W= r =-0.19W - 0.22T - 0.95C + e For group WC (N = 29): r = WO.69 To.748 CO.527 + e r = -0.62W - 0.28T - 0.66C + e
R2= 0.906 R2 = 0.966 R2 = 0.840 R2 = 0.978 R2 = 0.843
R2= 0.949
R2=0.891 R2 = 0.984
R2=0.854 R2 = 0.900
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KOUTSOPOULOS, MEYER & HENLEY
The coefficients of the linear model for the sample suggest cost as the most important factor in the aggregate decision, with waiting time and travel time of successively less importance. The group models, however, indicate that the aggregate model does not reflect the way decisions were actually made: the sample consisted of a set of quite discrete groups of decision makers, and no group model much resembles another or the aggregate model. All of the linear models provided higher values of R2 than did the multiplicative ones, despite the evidence from the interaction graphs for the latter as "correct." This apparent predictive failure of the multiplicative models is of primary methodological interest. Such a finding is not unique and was the subject of an article by Birnbaum [22], who indicated that an incorrect (poorly fitting) model sometimes provides better predictions of data than does a model that fits existing data better. Birnbaum showed that even when the data are perfectly multiplicative, comparison of correlation coefficients can lead to the erroneous conclusion that the linear model provides the better representation. Correlation coefficients can therefore be inappropriate for comparing additive and multiplicative models, because "the source of this difficulty lies in the assumption, implicit in the use of [the additive form], that the a priori values of [the variables] are positive and known to be on a ratio scale" [22]. Functional measurement, however, requires neither a priori values for the stimuli nor ratio scales for the responses. As a result of these and other advantages [14] of functional measurement over the correlational approach, it can be argued that if decision making is accurately captured by the measurement process, the model derived from interaction plots of the responses will predict better than any other.
Socioeconomic Characteristics of the Groups Data on socioeconomic characteristics and the actual health care utilization of the respondents were analyzed to see if such measures could serve as discriminants among the groups. Both sets of groups resulting from the euclidian-distance grouping algorithm were subjected to pairwise multiple discriminant analyses, using several sets of discriminating variables. Results from the two sets of groups were similar, although analysis of the three-group set was slightly more successful; thus only the result for the three groups "wait" (N = 41), "travel" (N = 9), and "cost" (N = 27) are presented. Discrimination was dearest between the "wait" and "travel" groups. A 13-variable model correctly assigned all 50 members; the variables that discriminated best were car availability (the "travel" group tended to have less access to an automobile), children (the "wait" group tended to have more of them), and current use of health care (the "travel" group tended to seek health care more often). A 12-variable model HEALTH correctly assigned 59 out of 68 members of the "wait" and "cost" SERVICES groups. These groups differed principally in car availability (the RESEARCH "cost" group had less access), age (the "cost" group tended to be older), 434 and current use of health care (the "cost" group sought care more
MODELING Table 2. Mean Responses of Three Groups on Socioeconomic and HEALTH DECISIONSCARE
Care-utilization Variables
Group Wait Cost (N = 41) (N= 27)
Variable
Age
...........................................
Sex (male=1, female=0) ........................... Years of education completed ...................... Houshold income per capita* ..................... Total children in household (younger than 18 and unemployed) ............ No. of preschool children in houshold. ........... dence in county ....................... Years of Full-time employment (yes=l, no=O). ............. Driver's licene (yes =1, no =) .................... Car availability (subjective scale
rating: "never" = 0, "always" = 20)
44.26
Travel (N = 9)
52.19 0.23 12.00 2.00
49.25 0.25 13.12 2.12
1.04 0.42 32.65 4..7 0.27 0.88 0.95
1.00 0 36.00 0.38 0.75
0.21 13.14 2.60 1.63 035 28A7
..............
19.37
17.31
14.12
No. of health care visits per year by all household members ...................... Per-visit cost of usual provider, $ ................... Distance to usual provder, miles .................. Usual time between making appointment
2.60 9.44 7.40
4.46 7.96 9.15
3.25 5.88 3.00
and seeing provider, days ..................... 4.28 Waiting time in usual provider's office, min ........ 26.65 More frequent care desired (yes=l, noO=0) ......... 0.19
1.23 32.38
1.88 23.12 0.62
0.19 Special health problem in household requing care more often than usual (yes= 1, no =0) 0.25 0.42 0.27 * Scored on categories: less than $3,000 = 1; $3,000-5,999 = 2; $6,000-8,999 = 3; $9,000-11,999 = 4; $12,000-14,999 = 5; $15,000-24,999 = 6; more than $25,000 = 7. .....
often). A seven-variable model correctly assigned 28 out of 36 members of the "travel" and "cost" groups. The chief discriminants were car availability (the "cost" group had greater access), children (the "cost" group had more children), whether respondents would seek more health care if they could (the "cost" group would seek more care), education (the "cost" group tended to have less), and income (the "cost" group tended to earn less). Group differences were also reflected in the means of the variables for each group, shown in Table 2. The "wait" group was younger, had more income, was more fully employed, had more children, and had come more recently to Cedar County. In contrast, the "cost" group was older and had less income. The "travel" group was composed of persons who lived dose to the health care provider they usually patronized and had less access to an automobile.
Discussion
The extent to which planning is successful in achieving uniform utilization of health services depends on its ability to adjust service delivery to accommodate consumer decision making. The methods illustrated in this artidle provide an approach to the study of consumer preference that can help clarify the adjustments needed. Modeling the formation of individual preferences for primary health care providers
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KOUTSOPOULOS, MEYER & HENLEY
offers a potentially useful tool for understanding the trade-offs among provider attributes on which consumer decisions are based. Further, the results suggest that differences in decision making, as measured in an experimental setting, are related to respondents' socioeconomic and behavioral characteristics. With further study it should be possible to predict the decision-making strategies of large populations on the basis of surveys of relatively small samples. Health care decisions are different in many respects from those treated in most consumer research: hence one would not expect an easy transfer of methods from one context to another. This research has illustrated some of the possibilities of the transfer of psychometric modeling techniques to the study of consumer health care decisions. Despite the many problems remaining unsolved, the results are promising and encourage further work in this direction.
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16. Koutsopoulos, K.C. and R.J. Meyer. Mass Transit Decision Making Market Segmentation: A Pilot Study. Technical Report No. 69, Institute of Urban and Regional Research, University of Iowa, 1976. 17. Louviere, J.J. and R.J. Meyer. Modeling consumer response to alternative shopping opportunities: A behavioral approach. Paper presented at the 1974 Annual Meeting of the West lakes Association of American Geographers, Atlanta, GA, Oct. 1974. 18. Anderson, N.H. Basic Experiments in Person Perception. Technical Report No. 43, Center for Human Information Processing, University of California at San Diego, 1974.
19. Anderson, N.H. Looking for configurality in dinical judgment. Psychol Bull. 78:93 Aug. 1972. 20. Koutsopoulos, K.C. Modeling Public Response to Rural Health Care Providers. Technical Report, Institute of Urban and Regional Research, Univenity of Iowa (forthcoming). 21. Ward, J.H. Hierarchical grouping to optimize an objective function. J Am Stat Assoc 58:236 Mar. 1963. 22. Bimbaum, MaH The devil rides again: Correlation as an index of fit. Psychol Bull 79:239 Apr. 1973.
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