Issues in Evaluating Importance Weighting in Quality of Life Measures

For most empirical research investigating the topic of importance weighting in quality of life (QoL) measures, the prevailing approach has been to use (1) a limited choice of global QoL measures as criterion variables (often a single one) to determine the performance of importance weighting, (2) a limited option of weighting methods to develop importance weighting, and (3) a limited number of domains to construct the (formative-indicator) measures. Although limitations resulted from a limited choice of global QoL measures as criterion variables to determine the performance of importance weighting and a limited option of weighting methods to develop importance weighting have been recognized previously, little attention has been paid to the impact of non-comprehensive domains in QoL measures constructed based on the formative-indicator approach. Using empirical data, this article revealed the potential impacts of non-comprehensive domains on the evaluation of importance weighting in QoL measures. Results presented in this article showed that both of the two most popular methods of evaluating the performance of importance weighting in QoL measures, correlation and moderated regression analysis, could produce misleading results in the situation when QoL measures constructed using the formative-indicator approach did not include comprehensive domains. Issues discussed in this article are of great importance to research in the field of QoL, especially on the topic of importance weighting in QoL measures.

1995; George and Bearon 1980;Myers and Diener 1995). There have been two major approaches to conceptualizing life satisfaction: the so-called ' 'top-down'' and ''bottom-up'' approaches (e.g., Diener 1984). The top-down approach assumes that global satisfaction is a predispositional trait or personality which influences one's evaluation of satisfaction in various areas of life. The bottom-up approach, on the other hand, conceptualizes global satisfaction as being influenced by one's evaluation of satisfaction in various life domains (Diener 1984). These two distinct approaches parallel the reflective-indicator and formative-indicator measurement models (Bollen and Lennox 1991). Although many popular life satisfaction measures (e.g., Life Satisfaction Index A, LSIA, by Neugarten et al. 1961; Satisfaction with Life Scale, SWLS, by Diener et al. 1985) follow the reflective-indicator model, life satisfaction can also be measured by combining satisfaction evaluations across discrete life domains (e.g., Campbell et al. 1976) which coincides with the bottom-up approach as well as the formative-indicator model.
However, it has long been observed that the correlation between life satisfaction or QoL measures using the reflective-indicator model and the formative-indicator model is far from perfect (e.g., Campbell et al. 1976;Cummins 1995Cummins , 1996Cummins et al. 1994;Hsieh 2003Hsieh , 2004Russell and Hubley 2005;Russell et al. 2006). One factor that may contribute to the discrepancy in correlation between QoL measures based on the two different measurement approaches has to do with the concept of valence, or the potential inter-person differences in perceived importance of different life domains (Hsieh 2011b). For QoL measures, especially life satisfaction measures based on the formative-indicator model, it has been a common practice to use a simple sum of satisfaction scores across various life domains to represent one's global life satisfaction (e.g., Campbell et al. 1976;Beatty and Tuch 1997;Mookherjee 1992). This summed-domains practice does not take into account the potential inter-person differences in perceived importance of different life domains. Researchers (e.g., Campbell et al. 1976;Inglehart 1978) have long noted the possibility of differential importance of different life domains in the overall picture of QoL. Different terms have been used to reflect the concept, such as (the most popular one) ''domain importance'' (Campbell et al. 1976), ''value priority'' (Inglehart 1978), and ''psychological centrality'' (Ryff and Essex 1992).
Although there appears to be a consensus that domain importance is not unimportant, debates over the need to incorporate domain importance, otherwise known as importance weighting, into measures of global life satisfaction remain (e.g., Campbell et al. 1976;Hsieh 2003Hsieh , 2004Mastekaasa 1984;Russell et al. 2006;Wu 2008a, b;Yao 2006a, b, 2007). Importance weighting is generally accomplished in one of three ways: One approach is to assign externally determined weights to various domains on a theoretical or conceptual basis. Although these weights reflect the concept of importance, the weights are applied to all respondents without taking into account any potential individual differences. A second approach is to consider regression coefficients as weights in a regression analysis when individual domain satisfaction scores are the predictor variables and a global QoL measure is the criterion variable. The results of this approach are heavily dependent on the criterion variable chosen and also do not take into consideration individual respondent differences. A third approach is to apply different domain importance weights to different respondents. This approach of importance weighting takes into account the potential individual differences in perceived importance of various domains and is the focus of this article.
Much of the controversy surrounding importance weighting has to do with existing empirical evidence. Specifically, many studies found that domain importance as a weighting factor failed to show any detectable increase in the power to explain variations in global QoL measures, in comparison with a simple sum of domain satisfaction scores (e.g., Campbell et al. 1976;Russell et al. 2006;Wu 2008a, b). For many who chose not to incorporate importance weighting, the decision was not conceptually based but empirically oriented. Opponents of importance weighting include those who purported that importance weighting was conceptually appealing. For example, in their landmark study, Campbell et al. (1976) attempted a number of different scoring systems and techniques of analysis only to find domain importance rating as a weighting factor failed to improve the total variances explained between global QoL instruments and domain satisfaction composites. Based on their empirical findings, Campbell et al. (1976) argued against the use of importance weighting due to the lack of empirical evidence to support a significant effect of domain importance as a weighting factor. Despite the findings, the role of domain importance in QoL measures continued to be as a study topic for many researchers (e.g., Hagerty and Land 2007;Hagerty et al. 2001;Hsieh 2003Hsieh , 2004Rojas 2006;Russell and Hubley 2005;Russell et al. 2006).
For most empirical research investigating the topic of importance weighting, the prevailing approach has been to use (1) a limited choice of global QoL measures as criterion variables (often a single one) to determine the performance of importance weighting, (2) a limited option of weighting methods to develop importance weighting, and (3) a limited number of domains to construct the (formative-indicator) measures (Hsieh 2003(Hsieh , 2004(Hsieh , 2011bRussell et al. 2006). Examples of applying this prevailing approach to examine the issue of importance weighting in the literature are easy to find. For instance, in arguing against importance weighting, Wu and Yao (2006a) examined the performance of importance weighting, based on a single global QoL criterion variable, measured by the Satisfaction with Life Scale (Diener et al. 1985), a small number of weighting methods and the 12 domains from the World Health Organization Quality of Life questionnaire (WHOQOL-100). Other examples following this similar approach to examine the issue importance weighting are abundant in the literature (e.g., Philip et al. 2009;Wu 2008a, b;Wu et al. 2009;Wu and Yao 2007).
However, it is important to note that there are at least three potential issues associated with the prevailing approach described above. Without properly acknowledging and addressing these issues, study findings on importance weighting may be interpreted incorrectly. Although two of these issues have been recognized previously, a third issue has not received sufficient attention in the literature. More specifically, only a small amount of studies recognized that using a limited number of domains to construct formative-indicator measures of QoL might influence the findings and our understanding of the topic of importance weighting (Hsieh 2003(Hsieh , 2004(Hsieh , 2011a. Unfortunately, none of these studies discussed what the impact of using a limited number of domains to construct formativeindicator measures of QoL on importance weighting might be. The purpose of this article is to first provide an overview of the two issues that have been recognized previously and then to discuss in greater detail using a limited number of domains to construct formativeindicator measures of QoL with empirical evidence. By focusing on the issue that has been largely neglected in previous studies, this article helps to bridge the gap in the literature on QoL research.

Issue One: Limited Choice of Criterion Variable
A discussion of the potential problem of using a limited choice of global QoL measures as criterion variables to determine the performance of importance weighting could be found Importance Weighting 683 in the study by Russell et al. (2006). Research on QoL is an area that keeps growing, and new measures of QoL continue to be developed (Evans 1994;Hagerty et al. 2001;Land 2000). There is no single agreed-upon ''best'' QoL measure. Although it is reasonable to assume that scores from different QoL measures should, to some degree, overlap, there is no reason to assume that all QoL measures capture identical constructs (Russell and Hubley 2005;Russell et al. 2006). The degree of overlap between QoL measures is likely to vary. Therefore, the association between any given two measures of QoL is unlikely to be the same. Varying degrees of discretion in correlation between different measures of QoL based on different conceptual and measurement approaches should be expected. As Russell et al. (2006) indicated, using a limited choice of global QoL measures as criterion variables (especially in the situation only a single criterion variable) to determine the performance of importance weighting could be problematic since there is no single QoL measure that is universally agreed-upon to be the criterion of QoL. Given the performance of importance weighting is likely to be related to the criterion variables chosen, considering multiple criterion variables would be beneficial as it can help to avoid potential judgment or misjudgment of the performance of importance weighting based on an arbitrary selection of a single criterion. More specifically, caution must be taken in interpreting findings from studies using a single QoL measure as the criterion variable to evaluate the performance of importance weighting. Any positive or negative findings from these studies should only be considered as the performance of importance weighting in relation to the particular criterion variable chosen and should not be generalized to any other QoL measures.

Issue Two: Limited Choice of Weighting Methods
The potential problem of using a limited choice of weighting methods to evaluate the performance of importance weighting has been pointed out previously (e.g., Hagerty et al. 2001;Hsieh 2003Hsieh , 2004Hsieh , 2011a. The weighting methods applied so far in the literature on importance weighting have mostly centered on the assumption of a linear function of domain importance scores (Hsieh 2011b). For example, surveying a group of injection drug users, Russell et al. (2006) evaluated importance weighting using the Injection Drug User Quality of Life Scale (IDUQOL) and found that scores of IDUQOL weighted by importance rating did not perform better than unweighted scores in measuring QoL. Using a 15-item satisfaction and importance measure, Wu and Yao (2006b) found that in a sample of undergraduate students, importance rating as a weighting mechanism did not improve the correlation between composite of domain satisfaction the Satisfaction with Life Scale (Diener et al. 1985). Both Wu and Yao's (2006b) and Russell et al.'s (2006) studies assumed a linear function of domain importance rating. As Hsieh (2003Hsieh ( , 2004 showed, the performance of importance weighting was dependent upon the weighting approaches applied. There is no reason to believe that the function of importance (weighting) must be a simple linear one. Decades ago, Campbell et al. (1976) suggested the possibilities of various types of weighting function of domain importance, such as ''hierarchy of needs,'' ''threshold,'' and ''ceiling.'' The ''hierarchy of needs'' approach suggests certain kinds of needs are more essential than others, and one would then expect that unless these most essential domains are reasonably satisfied, it probably does not matter much in terms of overall life satisfaction what happens in the less essential domains. The ''threshold'' approach suggests that overall life satisfaction depends on the presence of some threshold number of satisfactions. If the number of domains with which are satisfied does not meet this threshold, it is suggested the person would not feel satisfied with life as a whole. The ''ceiling'' approach suggests there is a top limit or ceiling to the number of domain satisfactions experienced by an individual, and satisfaction with domains beyond the top limit would not produce increased satisfaction with life as a whole. The actual weighting function of domain importance is unclear and is not necessarily limited to the functions discussed by Campbell et al. (1976). More recently, Rojas (2006) detailed the limitations and implications of an assumed linear relationship between global life satisfaction and domain satisfaction. As Rojas (2006) suggested, assuming a linear relationship between global life satisfaction and domain satisfaction would result in a loss of many features of the relationship and would clearly restrict our understanding of QoL.

Issue Three: Limited Number of Domains
The impact of using a limited number of domains to construct formative-indicator measures of QoL has not received much attention in the literature on importance weighting (Hsieh 2003(Hsieh , 2004. As indicated by Cummins (1996), there are at least 173 different domain names that have been used in the QoL literature, and the possible number of domains is even larger. To cover all possible domains of life in a single QoL measure is extremely unlikely, if not impossible. The number of domains covered in different QoL measures varies, depending on the focus of the measure. For example, the Quality of Life Index (QLI) by Ferrans and Powers (1985) covers the domains of health and functioning, social and economic, psychological/spiritual, and family. Mookherjee (1992), on the other hand, chose to cover the domains of residence, networking activities, family life, friendship, health and physical conditions, and financial situation. Since most QoL measures based on the formative-indicator model do not, or cannot, exhaustively cover all possible domains, it seems unrealistic to expect a perfect correlation between any given two QoL measures. In fact, given the countless potential of the number of domains that QoL measures can cover and the fact that many domains appear to overlap (Martin 2011), efforts to organize domains into a manageable number for efficiency purpose were not unreasonable (Cummins 1996). However, it is important to note that depending on the measurement model, not covering all possible domains in a measure can have different consequences. For measures that follow the reflective-indicator model, items or indicators in the measure should be interchangeable. Items or indicators should also have the same or similar content or share a common theme. Therefore, comprehensiveness of the domains covered in the measure is often not a major concern, given dropping items or indicators should not alter the construct measured. For measures that follow the formative-indicator model, items or indicators in the measure do not need to be interchangeable. Items or indicators also do not need to have the same or similar content nor share a common theme. Therefore, the extent to which the domains covered in the measure may be a cause for major concern, since not including or dropping indicators may alter the construct measured (e.g., Bollen and Lennox 1991;Diamantopoulos 2006;Diamantopoulos et al. 2008;Jarvis et al. 2003;MacKenzie et al. 2005;Hardin et al. 2011). Unfortunately, how the lack of comprehensiveness of domains included in QoL measures based on a formative-indicator model may influence the findings of importance weighting has not received much attention in literature on importance weighting in QoL measures. It is argued here that the lack of comprehensiveness of domains included in QoL measures using a formative-indicator model can lead to misleading results in evaluating the performance of importance weighting. In particular, the common analytical methods of evaluating the performance of importance weighting, correlation and moderated regression,  Folstein et al. 1975) were also excluded to avoid any potential problems that were the result of cognitive impairment. A trained graduate research assistant set up interview appointments, and faceto-face structured interviews were conducted by the research assistant at the homes of the participants. Most of the study participants were female (81%) and African American (92%). The mean age of the study participants was 76.4 (SD = 7.3), ranging from 62 to 94. The mean years of schooling completed were 9.8 (SD = 3.0), ranging from 2 to 16. Most of them were retired (96%) and had an annual household income below $15,000 (90%).

Domain Satisfaction and Importance
Participants were asked to rate their domain life satisfaction as: completely satisfied (coded 7), somewhat satisfied (6), slightly satisfied (5), neither satisfied nor dissatisfied (4), slightly dissatisfied (3), somewhat dissatisfied (2), or completely dissatisfied (1). A total of seven life domains were included: (a) health, (b) spare time, (c) financial situation, (d) neighborhood, (e) family life, (f) friendships, and (g) religion. Satisfaction with each domain was measured by responses to a single question. These seven questions were derived from Campbell et al.'s (1976) measures. Domain importance was measured by the same approach as Campbell et al. (1976). That is, participants were asked to rate the importance of each of the seven domains as: not at all important (coded 1), not too important (2), somewhat important (3), very important (4), or extremely important (5).

Global Satisfaction Criterion Variable
The Life Satisfaction Index A (LSIA) by Neugarten et al. (1961) was used to measure global life satisfaction. The LSIA is a 20-item measure designed to assess psychological well-being among older adults. This measure focuses on respondents' level of happiness and satisfaction with their present lives in general in comparison with the past and with lives of others. Following the scoring method proposed by Wood et al. (1969), two points were assigned for each positive answer, 0 for each negative answer, and one for each ''don't know'' answer. Previous studies reported that the internal consistency reliability of LSIA ranged from .66 (Serrano et al. 2004) to .80 (Wagnild 2003). The coefficient (Cronbach's) alpha was .77 for the current sample. In order to show the potential consequences of evaluating the performance of importance weighting in the situation where a formative-indicator measure with non-comprehensive domains was used, this analysis made an assumption that the seven domains included in the measure were comprehensive. The impacts of non-comprehensive domains on importance weighting could then be examined by constructing QoL scores with noncomprehensive domains (with six or less domains). Although a large number of QoL scores with non-comprehensive domains could be constructed (ranging from six domains to one domain) in the current case, results presented here were based on six and five domains. The impacts of non-comprehensive domains on importance weighting could be sufficiently demonstrated by the results with one-domain reduced (i.e., six domains) and two-domain reduced (i.e., five domains) measures. Two popular approaches used to evaluate the performance of importance weighting (Hsieh 2011a) were employed to explore the potential consequences of a formative-indicator measure with non-comprehensive domains.
First, a correlation analysis was used. The correlation analysis has been a popular approach to the evaluation of importance weighting (e.g., Hsieh 2003Hsieh , 2004Russell and Hubley 2005;Russell et al. 2006). In general, the performance of importance weighting is assessed by comparing the correlation between a criterion variable and the weighted score and that between the same criterion variable and the unweighted score, and a higher correlation is preferred. Based on the assumption made in this study, correlations between the scores with comprehensive and non-comprehensive domains would represent the impacts of measures with non-comprehensive domains. Both weighted and unweighted scores were produced for those with comprehensive and non-comprehensive domains. The unweighted scores were the simple sums of satisfaction scores across domains, while the weighted scores were the sums of the products of satisfaction scores (S) and importance scores (I) divided by the sum of importance scores ( P S 9 I/ P I) across domains. The unweighted full-domain score would represent the ''real'' QoL score under the assumption that global QoL score was a simple sum of domain satisfaction scores and importance weighting was unnecessary. On the other hand, the weighted full-domain score would represent the ''real'' QoL score under the assumption that importance rating served as a weighting factor in a linear fashion linking domain satisfaction to global QoL. Two types of reduced-domain scores were produced: one-domain reduced scores and two-domain reduced scores. One-domain reduced scores were the weighted and unweighted scores with six domains: DI -a to DI -g and S -a to S -g . The subscript indicated the domain eliminated, so S -a was the unweighted score with domain (a), health, eliminated, while DI -g was the weighted score with domain (g), religion, eliminated. Two-domain reduced scores were the weighted and unweighted scores with five domains: DI -ab to DI -fg and S -ab to S -fg . The subscript indicated the domains eliminated, so S -ab was the unweighted score with domains (a) and (b), health and spare time, eliminated, while DI -fg was the weighted score with domains (f) and (g), friendship and religion, eliminated. The correlations between unweighted satisfaction score with all domains (S) and unweighted satisfaction scores with reduced domains (S -a -S -g and S -ab -S -fg ) and weighted satisfaction score with all domains (DI) and weighted satisfaction scores with reduced domains (DI -a -DI -g and DI -ab -DI -fg ) were calculated.
Second, moderated regression analysis was also used to illustrate the impact of noncomprehensive domains on the performance of importance weighting. The analysis followed the three-step process outlined by Evans (1991). In general, the analysis would begin by estimating a regression model with global QoL as dependent variable and domain satisfaction of all the domains together as independent variables. The second step would be to add domain importance of all domains as independent variables. The third step would be to add to the second step the interaction/product terms of domain satisfaction by importance for all domains as independent variables (see Hsieh 2011a for detail). The change in R 2 from step two to step three would indicate the need for the inclusion of the interaction (i.e. domain importance weighting) terms. A significant increase in R 2 (indicated by the by F test) for the importance by satisfaction terms would indicate the need for including the interaction terms, and therefore, support importance weighting (see Evans 1991 for detail). For the current study, the dependent variable was the weighted score with all seven domains. This weighted full-domain score would represent the accurate QoL score, assuming the weighting function was correct. The impacts of non-comprehensive domains were demonstrated by excluding one or two domains of the independent variables. Following the same approach by Hsieh (2011a), the importance variables were constructed to reflect the weighting method (dividing the importance score of each domain by sum of the importance scores across all domains included, or I i / P I i ). Table 1 showed the correlations between scores with reduced domains, with full domains and LSIA scores. The correlation results for all one-domain reduced scores were presented. However, rather than presenting correlation results for all 28 two-domain reduced scores, Table 1 showed the correlations for selected results that illustrated the impacts of non-comprehensive domains in QoL measures. Based on the assumption made earlier that the seven domains were comprehensive, both weighted and unweighted fulldomain scores produced with all seven domains should represent the ''real'' QoL scores and should be the actual standards to be used for evaluating the performance of importance weighting. As shown in the left-hand columns in Table 1, a higher correlation between a one-domain reduced unweighted score and LSIA score did not necessarily mean a higher correlation between the one-domain reduced unweighted score and the full-domain unweighted score. For example, correlation between S -g and LSIA was .62 and between S -d and LSIA was .63, but correlation between S -g and the full-domain score was 1 and between S -d and the full-domain score was .98. The same could be found in the case of two-domain reduced unweighted scores. A higher correlation between a two-domain reduced unweighted score and LSIA score did not necessarily mean a higher correlation between the two-domain reduced unweighted score and the full-domain unweighted score. For example, correlation between S -be and LSIA was .57 and correlation between S -cd and LSIA was .60, but correlation between S -be and full-domain score was .95 and correlation between S -cd and full-domain was .91.
In the right-hand columns in Table 1, the same results could be found with weighted scores. That is, a higher correlation between a one-domain reduced weighted score and LSIA score did not necessarily mean a higher correlation between the one-domain reduced weighted score and the full-domain weighted score. For example, correlation between DI -a and LSIA was .40 and between DI -c and LSIA was .51, but correlation between DI -a and the full-domain score was .98 and between DI -c and the full-domain score was .88. Similarly, a higher correlation between a two-domain reduced weighted score and LSIA score did not necessarily mean a higher correlation between the two-domain reduced weighted score and the full-domain weighted score. For example, correlation between DI -ag and LSIA was .37 and correlation between DI -cd and LSIA was .53, but correlation between DI -ag and the full-domain weighted score was .97 and correlation between DI -cd and the full-domain weighted score was .78.
Next, moderated regression analysis was conducted for the weighted scores. The focus was to determine the contribution of the importance by satisfaction interaction terms via the change in R 2 (indicated by the by F test). Coefficients on specific domain satisfaction, domain importance, and satisfaction by importance of specific domains were not of interest. Similarly, rather than presenting a total of 28 regression analysis results, Table 2 showed the R 2 and R 2 changes for selected moderated regression analysis results that illustrated the impacts of non-comprehensive domains in QoL measures. Given that the dependent variable was the weighted score, one would expect to see the significant increase in R 2 (indicated by the by F test) for the importance by satisfaction terms in order for the moderated regression analysis to produce results that were not misleading. As shown in Table 2, the regression results for all of the one-domain reduced composites showed significant R 2 changes from step two to step three. Therefore, with current data, the moderated regression approach appeared to produce correct results in situations where only one domain was missing. However, as shown in Table 2, the regression results did not show significant R 2 changes from step two to step three for all of the two-domain reduced composites. The results indicated that when excluding financial situation (domain c) and family life (domain e), the moderated regression analysis produced an R 2 change from step two to step three that was not significant. Therefore, in situation where two domains were missing, the moderated regression approach could produce results that were misleading.

Summary and Discussion
In summary, our understanding of the topic of importance weighting in QoL measures has been limited by the use of (1) a limited choice of global QoL measures as criterion variables (often a single one) to determine the performance of importance weighting, (2) a limited option of weighting methods to develop importance weighting, and (3) a limited number of domains to construct the (formative-indicator) measures. Although limitations resulted from a limited choice of global QoL measures as criterion variables to determine the performance of importance weighting and a limited option of weighting methods to develop importance weighting have been recognized previously (e.g., Hsieh 2003Hsieh , 2004Russell and Hubley 2005;Russell et al. 2006), little attention has been paid to the impact of non-comprehensive domains in QoL measures constructed based on the formative-indicator approach. Using empirical data, this article revealed the potential impacts of non-comprehensive domains on the evaluation of importance weighting in QoL measures. Both of the two most popular methods of evaluating the performance of importance weighting in QoL measures, correlation and moderated regression analysis, could produce misleading results in the situation when QoL measures constructed using the formative-indicator approach did not include comprehensive domains. As shown earlier, the general practice of preferring higher correlation was not necessarily the best practice for evaluating the performance of importance weighting in QoL measures, particularly when the measures were constructed using the formative-indicator approach with noncomprehensive domains. The empirical example provided in this article revealed that a higher correlation between an arbitrarily chosen QoL criterion variable and either a weighted or unweighted non-comprehensive domain QoL score did not necessarily mean a higher correlation between the real weighted or unweighted full-domain QoL score and a weighted or unweighted non-comprehensive domain QoL score. In other words, using correlation as a method to evaluate the performance of importance weighting in QoL measures could be problematic when QoL measures constructed using the formative-indicator approach did not include comprehensive domains. In addition, empirical data presented in this article uncovered that results of moderated regression analysis would not necessarily capture the significant effect of the importance by satisfaction interaction terms in the situation when QoL measures were constructed using the formative-indicator approach with non-comprehensive domains. That is, even when importance weighting served as the actual function of linking domain satisfaction across various domains to global QoL, it was possible that results of moderated regression analysis would suggest otherwise in the situation when QoL measures were constructed using the formative-indicator approach with non-comprehensive domains. It should be noted that findings in this article could also be interpreted based on Hagerty and Land's (2007) work on the conditions under which the use of importance weights could improve the accuracy of composite QoL indices. As demonstrated by Hagerty and Land (2007), a statistical model for weighted QoL measures had two major properties: (a) an Table 2 Results of moderated regression analysis with reduced domains predicting weighted QoL scores with full domains Step 1 Step 2 Step 3 Satisfaction R 2 Importance DR 2 Satisfaction 9 importance DR 2 optimal composite QoL index could be achieved by using the population or sub-population average importance weights, and (b) in the absence of good information on domain importance, an equal-weighting method could be used and it was a so-called minimax estimator, as it minimized extreme disagreements on a composite QoL index. Based on the properties shown in Hagerty and Land's (2007) study, the weighting approach (although assumed to be correct) used in this article would be unlikely to produce an optimal composite. Issues discussed in this article are of great importance to research in the field of QoL, especially on the topic of importance weighting in QoL measures. As Hsieh (2011a) indicated, much of the argument against importance weighting was based on the empirical results of either correlation or moderated regression analysis (e.g., Wu and Yao 2006a, b). Unfortunately, most empirical evidence used to argue against importance weighting has not fully considered or acknowledged the potential impacts related to the issues discussed in this article, especially the issue regarding the limit number of domains included in the QoL measures. Therefore, it would be prudent to recognize that results from previous studies on importance weighting in QoL measures must not be interpreted without considering the the issues discussed in this article.