Soc Indic Res (2011) 104:427–437 DOI 10.1007/s11205-010-9752-y

Subjective Values of Quality of Life Dimensions in Elderly People. A SEM Preference Model Approach Paula Elosua

Accepted: 23 October 2010 / Published online: 31 October 2010  Springer Science+Business Media B.V. 2010

Abstract This article proposes a Thurstonian model in the framework of Structural Equation Modelling (SEM) to assess preferences among quality of life dimensions for the elderly. Data were gathered by a paired comparison design in a sample comprised of 323 people aged from 65 to 94 years old. Five dimensions of quality of life were evaluated: Health, Autonomy, Family and Social Support, Social Activities and Home Conditions. An unrestricted model was estimated and subjective preference values of dimensions were obtained. According to the subjective preferences, four groups of dimensions were established: Health-Autonomy-Home and Support-Social Activities. No differences among gender and age were found in the preference values. Keywords Thurstone

Quality of life  Elderly  Preferences  Structural equation modeling 

1 Introduction Quality of life in elderly people has become an important multidimensional construct which is studied from a variety of disciplines and which has significant effects on designing social policies for well-being. Its relevance is scientifically and socially accepted. Scientists assess it from a variety of disciplines (psychology, economics, sociology, biology, or medicine) and policy makers try to define social policies in order to improve the quality of life for the elderly. Quality of life is a dynamic construct (Allison et al. 1999) which varies among individuals and cultures (Carr et al. 2001). In each stage of the life cycle, it will have distinctive characteristics. The characteristics of each period are determined by demographic, political, social or historical aspects, and with reference to elderly people there are especially important dimensions related to health or social relationships (Bowling and Windsor 2001; Farquhar 1995; Fry 2000).

P. Elosua (&) University of the Basque Country, Avda. Tolosa, 70, 20018 San Sebastian, Spain e-mail: [email protected]

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Valid conclusions derived from quality of life studies depend on the psychometric properties of the measurement of this construct. The measurement includes two closely related aspects, construct-definition and measurement-methodology. Different definitions of quality of life, which include more general or specific dimension, can be found in the literature (see Gill and Feinstein 1994), and different methodological approaches can be followed to assess quality of life (Kind 2005; Feeny 2005). For now, there is no single, universally accepted definition of quality of life (Lauer 1999) but the present conception recognizes that quality of life is determined by personal/social factors as well as subjective/ objective factors. Related to elderly people, the five most cited factors are ‘‘health’’ (physical, psychological), ‘‘functional autonomy’’, ‘‘social activities’’, ‘‘family or social support’’ and ‘‘home and environment’’ (Bowling 1995; Cardona et al. 2003; Farquhar 1995; Ferna´ndez-Ballesteros and Zamarro´n 2006; Gabriel and Bowling 2004; Wiggings et al. 2004). Those five general domains are measured with items which cover them to a greater or lesser extent by including information about pain, mental illness, cognitive deterioration, levels of functional ability, well-being, beliefs, attitudes or emotions, societal support or environmental quality. According to recent reviews (Lauer 1999), most researchers accept that in order to assess quality of life both subjective and objective information is necessary. Much work has gone into the development of objective measures but there is less agreement on how to measure the subjective aspects (Ranzijn and Luszcz 2000). The objective information contributes to draw a general profile based on social, medical or economical indicators of quality of life but no information is given about well-being or about the relevance of the dimensions of quality of life to well-being. The objective information is, of course, important since it allows us to know the context and this is the first step towards designing policies to mediate in those domains which need to be improved. But this information would has to be completed. Subjective assessment of those domains gives us information about the relative importance of the factors determining the quality of life. This information is doubly important; it is individually pertinent and it is socially relevant. The subjective perspective lets us define individual profiles of quality of life by weighting the dimensions according to the subjective values, and having groupsubjective information enables the design of services and policies for improving quality of life, with emphasis on the most weighted dimensions. Several researchers have analyzed the subjective importance or preferences among quality of life dimensions in elderly people by using exploratory and qualitative methodology based on open or semi-open interviews. The results are tables based upon frequency that offer information about the subjective relevance of the dimensions of quality of life (Bowling 1995; Farquhar 1995; Nilsson et al. 1996; Wilhelmson et al. 2005). These works are important since they contribute to define more precisely the meaning of quality of life. However, it would be interesting to complete this information with quantitative values which help to understand and to analyze the subjective dimensions among groups. In order to get those subjective values formal measurement models are need. Thurstone (1927), Thurstone and Chave (1929) proposed a measurement model based on paired comparison experiments whose objective was to estimate the latent preferences of different stimuli. The model assumes that for a given stimulus there is one associated discriminal process or latent variable, and it offers a way to estimate the modal or mean value of this latent variable. In order to do that, Thurstone used the paired comparisons method: Given a set of stimuli, a multiple judgmental paired comparisons experiment consists of presenting all possible pairs of stimuli to each respondent and asks them to choose one object within each pair. Three assumptions characterized this model:

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(1) whenever a pair of stimuli (i, j) is presented to a respondent, it elicits a continuous preference; (2) within a pair, the stimulus whose preference is larger will be preferred by the respondent; and (3) the continuous preferences are normally distributed in the population. With n stimuli, there will be n(n - 1)/2 = k paired comparisons, and n latent variables will be estimated, with one latent variable for each stimulus. That is, quality of life factors and individuals may be scaled. In addition to scaling quality of life outcomes, Thurstonian method allow the scaling of individual respondents as well. Thus, although respondents need to provide only ordinal information, it is possible to estimate their underlying continuos responses. This approach seems more effective than asking respondents directly to provide a continuous rating which can be challenging task. The estimated individual judgments can be used effectively in identifying the determinants of the subjective evaluations. In the last few years, a lot of work has been carried out using Thurstone’s model. There are several interesting studies that were developed with this model in areas such as vocational preferences (Elosua 2007), risk perceptions (Florig et al. 2001; Morgan et al. 2001), food characteristics (Oakes and Slotterback 2002), and the evaluation of clinical services (Hazell et al. 2002). Until now, there has not been any work evaluating the topic of dimensions of quality of life. In this context, we wanted to analyze the subjective preferences among quality of life dimensions in elderly people using the Thurstonian approach in the Structural Equation Modelling (SEM) framework. In order to achieve this goal, we start with a brief description of the model, and then show the analysis and results derived from assessing quality of life dimensions preferences using paired comparison design. The results of this work are important, both methodologically and substantively. The methodology is significant because new perspectives are offered to assess the subjective aspects of quality of life. It is substantively noteworthy due to the fact that the results help to understand what aspects of quality of life are considered to be important by elderly people and we are able to quantify this subjective importance.

2 Thurstonian Model for Paired Comparison In paired comparison designs, two objects or stimuli (i and j) are presented simultaneously to the subject. For each presented pair the respondent has to select one object. The respondent will choose item i over item j if his or her latent preference for item (ti) i is larger than his or her latent preference toward item j (tj). The results of the comparison are coded as 1 or as 0, depending on the preference toward the first stimulus or the preference toward the last stimulus in the paired comparison, respectively.  1 if ti  tj ð1Þ yl ¼ 0 if ti \ti where l represents the (i,j) pair, yl is the observed response variable, 1 or 0, tj and ti are nonobserved or latent variables. The observed variable can be described by the difference between the latent preferences (t). Given that in a paired comparison there can exist instransitivities among preferences or choices, the model includes the error term (el). yl ¼ ti  tj þ el

ð2Þ

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where y*l is the latent response variable, tj and ti are non-observed variables or latent variables, el is the error term associated to the l pair. Following the assumptions about error in the framework of common factor model, the error variable (el) is assumed to be normally distributed, with a mean of 0 and variance x2, uncorrelated across pairs and uncorrelated with the latent utilities. The relation between the observed response variable (y), and the latent response variable (y*) is:  1 if yl  0 ð3Þ yl ¼ 0 if yl \0 Using the matrix algebra, we write the model in this way: y ¼ At þ e

ð4Þ

where e is a k 9 1 (k is the number of presented paired comparisons) vector of random errors with the covariance matrix, X2. This is a diagonal matrix with elements x21, x22,…, x2k and A is a k 9 n design matrix, where each column correspond to one of the stimuli and each row to one of the paired comparisons. For instance, when n = 3, the number of paired comparisons would be k = 3 and the matrix design would be as follows:    1 1 0    ð5Þ A ¼  1 0 1  0 1 1  The latent preferences and errors are normally distributed, and so the latent difference responses are also normally distributed.       lt t Rt 0 N ; ð6Þ e 0 0 X2 Their mean vector and covariance matrix are: ly ¼ Alt Ry ¼ ARt A0 þ X2

ð7Þ

where ly* is the vector of means of the latent differences responses,; lt is the vector of means of the latent preferences, A is the k 9 n design matrix, Ry* is the variance/covariance matrix of the latent differences responses, Rt is the variance/covariance matrix of the latent preferences, A’ is the transposed matrix of A, X2 is the diagonal covariance error matrix. To obtain the thresholds and tetrachoric correlations in regards to the paired comparison, the latent differences response vector has to be standardized. With this standardization, the z* matrix is created.   ð8Þ z ¼ D y  ly P where D = [Diag( y*)]-1/2, the standardized responses are normal with P latent differences P mean 0 and correlation matrix, Pz* = D( y*)D = D(A tA’ ? X2)D. The estimate of this model is considered equivalent to the estimation of a structural equation model for dichotomous variables (Maydeu-Olivares and Herna´ndez 2005). The design matrix (A) is similar to the loading matrix, the means of the latent preferences (lt) are the factor means, the correlation matrix among factors is the Pt matrix, and the error diagonal (X2) matrix is the unique factor matrix.

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Although the specification of the model has been shown on the paired comparison design, it would be easy to extend it in order to cover another Thurstonian model, the ranking data. In a ranking data design, all choice alternatives are presented at once and the subject has to rank order them. Any ordering can be coded equivalently using k paired comparisons, although the inverse is not true. In the rank order task, there is no chance for intransitivities, but they are possible in the paired comparison tasks. This difference is the reason for introducing the ‘‘error’’ term in Eq. 2.

3 Method 3.1 Participants Data were collected from 323 retired people. The age range spanned from 60 to 94. Among the total sample 140 were men (Mean = 70.86; SD = 10.65) and 181 were female (Mean = 71.40; SD = 10.28). (For description see Table 1). The participants were recruited through volunteer associations and social clubs for the elderly in Spain. The participants were informed about the objectives of this project and their participation was totally voluntary. A group of trained psychologists was responsible for administering the questionnaire although some of the participants chose self-administration. No problems were reported in filling in the questionnaire. 3.2 Measures The instrument, 65QOL, was specially constructed for this study. The main aim of the 65QOL questionnaire was to assess the quality of life of elderly people in five dimensions related to health, functional autonomy, social and family nets, home and environmental conditions and social activities. One of the items of 65QOL was constructed based on the Thurstonian approach to the measure of preferences. In this design 10 statements were assembled by comparing two dimensions at a time (see Table 2). For each pair of elements the respondents must choose one, and this preferential selection represents the subjective preferences related to the quality of life dimension. 3.3 Analysis In order to get the preference values, we fit one unrestricted lineal factor model to the data with binary dependent observed variables (Fig. 1). The estimation method used was the weighted least square measurement method (WLSM). This model was implemented and Table 1 Description of the sample

Age

Males

Females

Total

60–64

5

14

19

65–69

43

52

95

70–74

43

49

92

75–79

37

44

81

80–84

10

14

24

85–94

3

9

12

141

182

323

Total

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Table 2 Thurstonian paired comparison design To achieve a good quality of life the most relevant to me is: … Having good health

Having social and group activities

Having personal autonomy

Having family and social support

Having social and group activities

Having family and social support

Having family and social support

Having good health

Having personal autonomy

Having social and group activities

Having social and group activities

Having a home adapted to my needs

Having a home adapted to my needs

Having family and social support

Having personal autonomy

Having good health

Having a home adapted to my needs

Having personal autonomy

Having good health

Having a home adapted to my needs

y12*

y13*

y14*

t1

y15*

t2 y23*

y24*

y25*

t3

t4

y34*

t5 y35*

y45*

Fig. 1 Covariance Structure Model

estimated by Mplus (Muthe´n and Muthe´n 2001). After the estimation, we retrieved the mean latent values for the stimuli, as well as the latent values for the participants in each quality of life dimension.

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3.4 Results 3.4.1 Latent Preferences For identification purposes we fixed the latent value of the Social Activities dimension at 0, and we fixed to 0 the covariances related to this dimension of Social Activities (MaydeuOlivares and Herna´ndez 2005). The results of the analysis showed good fit between the model and the data (v2 = 52.76; df = 32; p = 0.01; RMSEA = 0.048). The estimates and standard error for the latent preferences are shown in Table 3. The most valued dimension was Health, whose estimated latent value was 6.27. The Personal Autonomy dimension was considered the second most relevant dimension by the elderly sample (1.88). The difference between the first dimension and the second one was the biggest difference found among the analyzed factors. Having social and family support was evaluated with 0.98 for the sample, and having an adequately adapted home (0.82) was the following dimension. Finally the 0 point in the scale of preferences was occupied by the dimension related to social activities. The estimated factor scores represent the quality of life preferences for each participant. The Fig. 2 show the profile for 5 persons who were randomly selected from the total sample. According to the estimated parameter values and to their standard errors, confidence intervals were computed for each latent preference in order to study the differences among latent preferences. Given the confidence intervals, the ordering of the quality of life preference latent means could be sorted into four groups. The first group would be composed of the preferences regarding Health. The second would include Personal Autonomy. The third place was for Home and Support; the latent mean difference values for the two dimensions were non statistically significant. The respondents put the dimension related to social activities in last place. 3.5 Differences Among Gender and Age 3.5.1 MIMIC Model In order to evaluate the effect of gender on preferences a MIMIC model was defined by including effects on the latent factors. The results of the analysis showed good fit between Table 3 Estimated latent means and standard errors Health

Autonomy

Support

Activity

Home

6.27 (1.93)

1.88 (0.33)

0.98 (0.18)

0 (fixed)

0.82 (0.17)

Male

5.72

1.56

0.81

0.09

0.71

Female

6.22

1.74

1.05

-0.02

0.75

65–69

6.05

1.78

0.95

0.00

0.73

70–74

6.08

1.55

0.98

0.02

0.75

75–79

5.87

1.66

0.88

0.07

0.72

80–94

6.01

1.66

0.77

0.10

0.88

85–99

6.01

1.86

1.21

0.16

0.45

Latent means Gender

Age

Standard errors are in parentheses. Bold numbers are significant results (p \ 0.01)

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Preference-Values

8

6

4

2

Home

Activity

Support

Autonomy

Health

0

Fig. 2 Individual profiles

the model and the data (v2 = 52.76; df = 32; p = 0.011; RMSEA = 0.048), and lack of significant effect of the gender covariate on the latent means (chealth = -0.701; Se = 0.44; cautonom = -0.08; Se = 0.21; csupport = -0.13; Se = 0.23; cactivities = 0.079; Se = 0.18; chome = -0.07; Se = 0.18). Latent mean differences across gender and age. Latent preference values were estimated for each respondent and differences in latent mean values across groups (Gender 9 Age) were analyzed under the General Linear Model. The preference means for each group can be read in Table 3. The results showed lack of significance among the latent means differences and non interaction among gender and age (p [ .05; the values of the statistical tests are not shown). The estimated preference values and the order of latent preferences were equivalent among gender and age; so the values were independent of both factors. Figure 3 represents the mean values estimated by gender. Although the differences were non significant, the analysis showed that for Health, Autonomy, Support and Home the means were slightly higher for females, whereas the latent mean value for the dimension related to social activities was higher for the male sub-sample.

4 Discussion Regarding the objectives of this work, the discussion is organized into two parts. The first is related to the subjective measures of quality of life and the second explores the advantages and disadvantages of the methodology used in this investigation. In interpreting the results of this study it is important to explain that the sample of participants is representative of a population of elderly people who live at home and

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7 Male

6

Female

5 4

3 2

1 0

Health

Autonomy

Support

Activities

Home

Fig. 3 Latent preferences by gender

maintain a medium–high level of social activity, as they were recruited in social clubs and volunteering organizations. The sample showed differential income levels (v2df ¼5 =59.14; p \ 0.01) as well as differential educational levels (v2df ¼3 =14.12; p = 0.003) for gender, with the male sub-sample showing higher levels than the female sub-sample in both variables, income and educational level. The preference values were estimated relatives to the dimension associated with social activity which was fixed to 0 (‘‘Having social and group activities’’). The most relevant dimension in maintaining a good quality of life was health. The second dimension was personal autonomy. The subjective distance between health and autonomy was the largest one found among the evaluated dimensions. The third place was occupied by two different aspects related to quality of life: having an adequately adapted home and maintaining social and family support. The subjective values for these two dimensions were indistinguishable. Finally, the last dimension was the one related to the maintenance of social activities. This general order among quality of life dimensions is not concordant with the results reported in several exploratory studies which concluded the importance of non-health dimensions in quality of life (Bowling 1995; Farquhar 1995; Wilhelmson et al. 2005). However, from a methodological point of view, the results’ comparability depends on the comparability of the methods and needs to consider the characteristics of the analyzed culture (Elosua and Hambleton 2009). Regarding the first factor, it is clear that by using different ways of gathering data it is possible to find a different order among the dimensions. In the same study, Wilhelmson et al. (2005) report different results on the same sample by using different methods. On the other hand, given the cultural and social factors affecting the quality of life it is not surprising that we can find a different order among dimensions in different cultures. In assessing cross-cultural differences-similarities among quality of life dimensions, it should be necessary to use the same methodological instruments and the same formal model. In order to derive conclusions about equality/differences between cultures or groups, using different instruments and different models is not correct.

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It is significant to mention also that non differences were found among age and gender in evaluating the subjective values of quality of life dimensions. The same formal model was applied to the data and non differences were found among the estimated subjective values. The general values can be considered equivalent, even when we found differences in economic conditions and educational level among gender. These differences did not have any significant effect on the subjective preference values. From these general results we would like to highlight the subjective value given to the dimension related to home. This result agrees with the aspiration to age in place, which has been extensively documented in the gerontological literature (Gitlin 2003). It is recognized from the World Health Organization that an important goal in ageing healthily is to create environments supporting healthy living and well-being, and in this sense the role of housing is especially important. Particularly in old age, much time is spent at home and personal autonomy, which is the second dimension in relevance, strongly depends on having an adapted physical environment. Promoting adequately adapted housing is one strategic approach for improving the quality of life by preserving autonomy, identity and, therefore, healthy ageing. In relation to the methodological approach used, we would like to comment two aspects of this investigation with regard to the mathematical model. We used the Thurstonian model for the paired comparisons. This is an older method for modelling preferences, which we used to analyze the subjective values of dimensions of quality of life, of one elderly sample from a new perspective. (1) The estimation process is based on the five descriptors of the latent domains. Domain descriptors must be carefully defined and selected in the preference choice task since the validity of the inferences will depend on how well the descriptors represent the target domains and cover the construct. (2) The estimation of latent preferences was carried out in the Structural Equation Modelling framework. The Thurstonian approach enables us to work with estimated latent variables instead of observed variables, and to incorporate covariates to the model in order to explain individual differences. Using paired comparison designs, minimal constrictions on the response behaviour of a respondent are imposed. Particularly when differences between choice alternatives are small, this method provides more information about individual preferences than is obtainable using summative scales (Maydeu-Olivares and Bo¨ckenholt 2005). If the fit between the model and the data is good, this approach can be used in order to obtain profiles for each respondent, and so it would improve the traditional approach used to create those outputs. In short, the use of this framework would improve the assessment of the preferences by making an interesting link between the observed data and the measurement model. This allows for the incorporation of explicative variables in the model, as well as using a method for collecting data that provides more information about individual preferences. There are several important applications of this method (Maydeu-Olivares and Bo¨ckenholt 2008), but not related to the topic of the quality of life. However, the quality of life topic can be modelled through this form of measurement and we strongly encourage researchers to use this approach. Acknowledgments This research has been partially supported by MICINN (PSI2008-856) and by the University of the Basque Country (GIU09/22).

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