Testing the Convergent and Discriminant Validity - Semantic Scholar

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Health Cons. Smoking stinks.a. Aesthetic Cons. Smoking is a messy habit.a ..... Relationships between overall and life facet satisfaction: A multitrait–multimethod ...
Psychology of Addictive Behaviors 2008, Vol. 22, No. 2, 288 –294

Copyright 2008 by the American Psychological Association 0893-164X/08/$12.00 DOI: 10.1037/0893-164X.22.2.288

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Testing the Convergent and Discriminant Validity of the Decisional Balance Scale of the Transtheoretical Model Using the Multi-Trait Multi-Method Approach Boliang Guo, Paul Aveyard, and Antony Fielding

Stephen Sutton

University of Birmingham

University of Cambridge

The authors extended research on the construct validity of the Decisional Balance Scale for smoking in adolescence by testing its convergent and discriminant validity. Hierarchical confirmatory factor analysis multi-trait multi-method approach (HCFA MTMM) was used with data from 2,334 UK adolescents, both smokers and non-smokers. They completed computerized and paper versions of the questionnaire on 3 occasions over 2 years. The results indicated a 3-factor solution; Social Pros, Coping Pros, and Cons fit the data best. The HCFA MTMM model fit the data well, with correlated methods and correlated trait factors. Subsequent testing confirmed discriminant validity between the factors and convergent validity of both methods of administering the questionnaire. There was, however, clear evidence of a method effect, which may have arisen due to different response formats or may be a function of the method of presentation. Taken with other data, there is strong evidence for construct validity of Decisional Balance for smoking in adolescence, but evidence of predictive validity is required. Keywords: decisional balance, hierarchical confirmatory factor analysis multi-trait multi-method approach (HCFA MTMM), convergent validity, discriminant validity

1993; Marsh & Grayson, 1992; Marsh & Hocevar, 1983, 1988; Stacy, Widaman, Hays, & DiMatteo, 1985; Widaman, 1985). Confirmatory factor analysis (CFA) is used frequently to analyze the MTMM matrix (CFA MTMM). With CFA, a priori trait and/or method factors are posited. Factors defined by different measures of the same trait suggest construct validity of the trait. Factors defined by measures assessed by the same method suggest method effects. CFA MTMM also tests the fit of the overall model to the data. In CFA MTMM studies, models with method factors only are fit and compared with models with correlated traits and correlated methods. Convergent validity is shown if the method only model does not fit well. There are no universally accepted criteria to support discriminant validity in CFA MTMM (Marsh, 1988; Marsh & Hocevar, 1988). Although some have argued that correlation between trait factors provides evidence against discriminant validity (Widaman, 1985), trait correlation is typical in MTMM studies. High trait correlations indicate lack of discriminant validity (Kenny, 1979; Marsh & Hocevar, 1988), while low correlations between trait factors indicate discriminant validity. In CFA MTMM analysis, discriminant validity is therefore tested by setting the correlation among trait factors to 1.0, which is the equivalent of a single factor model, to see whether this model fits better than the model where the trait factor correlations are freely estimated. If it does not, discriminant validity is supported (Kenny, 1979; Marsh & Hocevar, 1988; Stacy et al., 1985). In traditional CFA MTMM analysis, multiple items reflecting each scale are summed or averaged to scale scores for analysis, and CFA is used to fit method and trait factors. This assumes that the actual factor structure accurately reflects the a priori structure,

Convergent validity is agreement between measures of the same construct assessed by different methods. Discriminant validity refers to the distinctiveness of different constructs (Campbell & Fisk, 1959). Convergent validity and discriminant validity can be explored by the multi-trait–multi-method (MTMM) analysis, in which two or more traits are each assessed by two or more methods (Campbell & Fisk, 1959; Marsh & Grayson, 1992; Schmitt & Stults, 1986). Different measures of the same trait should correlate highly with each other but should correlate less strongly with measures of distinct traits (Widaman, 1985). Campbell and Fiske’s decision rules for inferring convergent and discriminant validity from MTMM matrixes were qualitative, and they used observed variables’ correlations to draw conclusions about underlying trait and method factors with little attention to true trait correlation (Marsh, 1988). More quantitative approaches to MTMM analysis have been proposed (Hau, Wen, & Cheng, 2005; Kenny & Kashy, 1992; Marsh, 1988, 1990; Marsh & Byrne,

Boliang Guo and Paul Aveyard, Division of Primary Care & Public Health, University of Birmingham, Birmingham, United Kingdom; Antony Fielding, Department of Economics, University of Birmingham; Stephen Sutton, Department of Public Health and Primary Care, Institute of Public Health, University Forvie Site, University of Cambridge, Cambridge, United Kingdom. This study was supported by Cancer Research UK Grant C9278/A5639. Correspondence concerning this article should be addressed to Paul Aveyard, Department of Primary Care and General Practice, University of Birmingham, Birmingham B15 2TT, United Kingdom. E-mail: [email protected] 288

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without testing whether it is actually appropriate (Marsh, 1988). An alternative approach is hierarchical CFA in MTMM (HCFA MTMM). This fits a first order factor structure where each factor loads on its contributory items. Consequently, it can confirm that the theoretical factor structure is actually supported by the data. Second order factors representing trait and method are then fit (Lance, Noble, & Scullen, 2002; Marsh, 1988; Marsh & Hocevar, 1988). In this study, we use HCFA MTMM to explore the convergent and discriminant validity of the Decisional Balance Scale of the Transtheoretical Model (TTM). The TTM holds that individuals progress through qualitatively distinct stages when changing behaviors such as smoking cessation (Prochaska & Velicer, 1997). Precontemplation is the stage where change is not intended in the foreseeable future. Contemplation and preparation then lead into action, for example, stopping smoking, which leads to maintenance when change is consolidated. There are four independent constructs: self-efficacy, temptation, decisional balance, and the processes of change. The precise structure of the TTM is not fully described, but it is clear that all of these independent constructs cause stage movement. In one article, the TTM developers suggested that the processes of change are the independent variable and that other cognitive variables, such as decisional balance, are mediators (Velicer, Rossi, Diclemente, & Prochaska, 1996). Nevertheless, the strong principle of change is that a one standard deviation increase in pros of health behavior change is necessary to move from precontemplation to action. The weak principle is that a half a standard deviation decrease in cons is necessary for the same move (Prochaska, 1994). Other stage theories exclude the processes of change, and decisional balance is of even greater importance as a driver of stage movement (Dijkstra, Conijn, & De Vries, 2006). Sutton proposed an important test of stage theory (Sutton, 2005). An ideal study should apply a matched intervention to one group and a mismatched intervention to another. In these studies, decisional balance could be used as the basis of the matched/ mismatched intervention (Dijkstra et al., 2006). Assuming the matched intervention is more effective, a study should further show that the effect of the intervention was mediated by the proposed drivers of change, in this case decisional balance. If such an ideal is to be reached, it is important to show that decisional balance can be measured validly. The measure of decisional balance was first derived from the work of Janis and Mann (1977; Velicer, Diclemente, Prochaska, & Brandenburg, 1985). Velicer et al. (1985) tested a 24-item questionnaire of the pros and cons of smoking with two response formats—frequency and importance (Velicer et al., 1985). Both response formats gave nearly identical results on principal components analysis and gave a two-component solution. For adults, the items focus on smoking’s pharmacological benefits (the pros) and health risks and embarrassment (cons). The Decisional Balance Scale has been subsequently used with the importance response scales but also with the agreement scales for some behaviors in adults (Prochaska et al., 1994). Stern, Prochaska, Velicer, and Elder (1987) developed the adult questionnaire into a six-item pros and a six-items cons measure for adolescent smoking, though details of this process are described in an unpublished thesis (Stern et al., 1987). Pallonen, Prochaska, Velicer, Prokhorov, and Smith (1998) investigated the factor struc-

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ture of decisional balance for adolescence and found a single cons factor with two pros factors—Coping Pros and Social Pros (Pallonen et al., 1998)—that were each first order factors. Details of the model fitting and alternative models pursued were not described. Migneault, Velicer, Prochaska, and Stevenson (1999) developed a measure of decisional balance for adolescent drinking and found that a two-factor solution (Pros and Cons) and a threefactor solution (Pros, Cons-Potential, and Cons-Actual) fit equally well (Migneault et al., 1999). The most comprehensive investigation of decisional balance in adolescent smoking is described by Plummer et al. (2001). They fit sequentially one-, two-, and three-factor models for both smokers and non-smokers separately and found that the three-factor solution was preferred, once again finding pros divided into Social and Coping Pros. However, fit of these models was only moderately good, with comparative fit indices (CFIs) of 0.957 and root-mean-square error of approximation (RMSEA) of 0.070 for smokers and a CFI of 0.963 and RMSEA of 0.055 for non-smokers. Other models were not explored. These investigators found differences in the means of these constructs between stages in a cross-sectional sample that were somewhat consonant with expectations from the TTM, as did Pallonen et al. (1998), which might be interpreted as weak evidence of predictive validity. Thus far, therefore, there is limited validity testing of this key construct in the TTM in adolescents. We therefore used CFA MTMM to explore the convergent and discriminant validity of the measure.

Method Participants The data were collected as part of a randomized controlled trial of smoking prevention and cessation (Aveyard et al., 1999, 2001). In the autumn of 1997, 26 intervention schools’ Year 9 (ages 13–14 years) pupils completed a baseline paper questionnaire and also used the interactive computer program on the same day. Decisional Balance and other scales were tested in both the paper and computer questionnaires. These participants used the program three times, once in each term of 1997/1998, and were subsequently followed up with paper questionnaire tests 1 and 2 years later. Thus, they participated three times in a computer questionnaire session and three times in a paper questionnaire session. There were 2,334 of 4,125 (57%) students without any missing values in Decisional Balance testing available for analysis.

Measures The items and the associated factors are shown in Table 1. In a currently unpublished manuscript, we found that a four-factor solution as outlined in Table 1 fit the data significantly better than the three-factor solution found by Pallonen et al. (1998) and Plummer et al. (2001). However, the paper questionnaire omitted the Aesthetic Cons, so a three-factor solution of Social and Coping Pros and Health Cons was used in this analysis. The only difference between the two formats of questionnaire was the response categories—agreement in the paper questionnaire, like Pallonen et al. (1998), and importance in the computerized version, like Plummer et al. (2001).

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Table 1 Items in the Adolescent Smoking Decisional Balance Scale and Their Associated Factors Item Smoking makes people get more respect from others. Teenagers who smoke have more friends. Teenagers who smoke have more boy/girlfriends. Smoking helps people to cope better with frustrations. Smoking cigarettes is pleasurable. Smoking cigarettes relieves tension. Smoking can affect the health of others. Smoking cigarettes is hazardous to people’s health. Cigarette smoke bothers other people. Smoking stinks.a Smoking is a messy habit.a Smoking makes teeth yellow.a a

Factor Social Pros Social Pros Social Pros Coping Pros Coping Pros Coping Pros Health Cons Health Cons Health Cons Aesthetic Cons Aesthetic Cons Aesthetic Cons

Not included in the paper questionnaire so omitted from these analyses.

Analytical Procedure The data were longitudinal in nature and were accommodated by stacking measurement occasions so that the measures from each occasion loaded onto each of the second order trait and method factors. The models below were set and tested sequentially in our study with Mplus 4 (Hau, Wen, & Cheng, 2005; Lance et al., 2002; Lance & Sloan, 1993; Mars & Grayson, 1992, Marsh & Hocevar, 1988; Widaman, 1985). Model 0 (M0): A first order CFA model as the target model for subsequent modeling was fit. A test of this model supported the prior three-factor structure of Pros and Cons and justified the interpretation of trait factors in subsequent hierarchical CFA models (Marsh & Hocevar, 1988). Model 1 (M1): Based on M0, the second model is the HCFA MTMM correlated trait correlated method model (CTCM). In this model, the correlations between second order trait factors and method factors were fixed to zero, but correlation between trait factors and correlation between method factors were estimated freely (Lance et al., 2002; Marsh, 1990). The model is shown in Figure 1, and this model is the basic model for HCFA MTMM testing and must be supported to allow further testing of discriminant and convergent validity. Model 2 (M2): Based on M1, M2 is a method only model, for which no second order trait factors shown in Figure 1 were included in the model, and was set for the convergent validity test. Model 3 (M3): M3 is based on M2. All second order trait factor correlations were fixed to 1 for the discriminant validity test. Judgment of the goodness of fit was based on indices used in structural equation modeling. Non-significant ␹2 generally indicates the model fits the data well. However, ␹2 is sensitive to large sample size effects. Consequently, we also used CFI, non-normed fit index (NNFI), RMSEA, standardized root-mean-square residual (SRMR), and Akaike information criterion (AIC) as model fit indices (Hagenaars & McCutcheon, 2002; Hau et al., 2005; Wen, Hau, & Marsh, 2004). Values of CFI and NNFI larger than 0.90 indicate acceptable fit. Values of RMSEA and SRMR less than 0.08 also indicate good fit. A model with a smaller AIC is preferred to one with a larger AIC.

Results All model fit indices are shown in Table 2. For M0, although ␹2 was significant, indicating lack of perfect fit, this was expected due to the large sample size (Hau et al., 2005; Vandenberg & Lance, 2000; Wen et al., 2004). Thus this should not be taken as a “poor fit” of the underlying approximate model. Other model fit indices satisfied the general guidelines for a reasonable fitting model. Inspection of the factor loadings and the factors variance/ covariance indicated that each first order factor was well defined, indicating that HCFA MTMM should continue. M1 showed that the HCFA MTMM CTCM model fit the data acceptably. The CFI was 0.903, NNFI was 0.896, RMSEA was 0.039, and SRMR was 0.049 (Table 2). Based on the modification index, we correlated the second and third occasion paper questionnaire item 6. This is justified because those two items were repeated measures (Joreskog & Sorbom, 1993). Doing this, both CFI and NNFI were greater than 0.900, RMSEA was 0.038, and the SRMR was 0.049. The AIC decreased to 301,339 from 301,564. All factor loadings on the second order trait factors and second order method factor were statistically significantly different from zero. The variance/covariance of trait factors and method factor were also statistically significant. Detailed results are shown in Tables 3,4, and 5. M1 indicated that the two measures of the same item, one from the computer questionnaire and one from the paper questionnaire, loaded on a single trait factor for each of the three decisional balance factors. In other words, the three-factor solution of Social Pros, Coping Pros, and Health Cons was supported when either the paper or the computerized questionnaire was used. Furthermore, the model also showed evidence of method factors, in that measures by the same format of questionnaire also significantly loaded on a single method factor. M2 tested convergent validity by testing the fitting of the method only model and comparing its model fitting with the fitting shown in M1. The method only model did not fit the data as well as the low CFI and NNFI values indicated. Thus, convergent validity for Decisional Balance was supported. In M3, we constrained all correlations between trait factors to 1 to test the discriminant validity. The latent variable covariance matrix in this model was not positive, indicating the one trait factor model is not appropriate. Hence the results supported discriminant validity of traits in the Decisional Balance Scale.

Discussion For adolescent smoking, we found that a three-factor solution fit the data best, as others have found (Pallonen et al., 1998; Plummer et al., 2001). Thus far, research has proposed then confirmed factorial validity. These results extend these findings by producing evidence of convergent validity. Whether assessed by the computerized questionnaire or the paper questionnaire, and whether the response format was agreement or importance, the items loaded on the first order trait factors. The fit indices showed strong evidence of convergent validity. However, there was clear evidence also of discriminant validity, as shown by lack of fit when all correlations among trait factors were constrained to be one. Plummer et al. (2001) showed a high correlation between the Social Pros and Coping Pros factors, as might be expected (Plummer et al., 2001). If we follow traditional MTMM principles as

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Figure 1. Hierarchical confirmatory factor analysis multi-trait multi-method correlated trait correlated method model. Soc ⫽ first order Social Pros; Cop ⫽ first order Coping Pros; Health ⫽ first order Health Cons; PC ⫽ computer questionnaire; Paper ⫽ paper questionnaire; 1 ⫽ Time 1; 2 ⫽ Time 2; 3 ⫽ Time 3.

Table 2 Fit Indices for Alternative Models in HCFA MTMM Analysis Model

df

␹2

p – ␹2

CFI

NNFI

RMSEA

First order CFA HCFA MTMM CTCM Method only One trait factora

1224 1337 1358 1345

4,974.528 6,004.474 8,678.078 9,814.377

.000 .000 .000 .000

.940 .903 .847 .823

.929 .896 .839 .812

.036 .039 .048 .052

SRMR .032 .049 .074 .564

Note. HCFA MTMM ⫽ hierarchical confirmatory factor analysis multi-trait multi-method; CFI ⫽ comparative fit index; NNFI ⫽ non-normed fit index; RMSEA ⫽ root-mean-square error of approximation; SRMR ⫽ root-mean-square residual; CFA ⫽ confirmatory factor analysis; CTCM ⫽ correlated trait correlated method model. a Model 3: The latent variable covariance matrix is not positive definite.

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292 Table 3 Second Order Factor Loading and Variance/Covariance in Confirmatory Factor Analysis Multi-Trait Multi-Method Correlated Trait Correlated Method Model Variable

Social Pros

Coping Pros

Health Cons

PC

Paper

Loadings of items on traits and methods SOC-PC1 SOC-Paper1 SOC-PC2 SOC-Paper2 SOC-PC3 SOC-Paper3 COP-PC1 COP-Paper1 COP-PC2 COP-Paper2 COP-PC3 COP-Paper3 HEAL-PC1 HEAL-Paper1 HEAL-PC2 HEAL-Paper2 HEAL-PC3 HEAL-Paper3

.291 .768 .214 .630 .078 .564

.540 .275 .791 .522 .917 .472 .762 .284 .733 .149 .606 .119

.276 .493 .472 .882 .591 .747 .477 .768 .559 .631 .445

⫺.141 ⫺.264 ⫺.446

.754 ⫺.058 ⫺.321 ⫺.288

Variance–covariance matrixes of traits and methods factors Social Pros Coping Pros Health Cons PC Paper

.025 .095 ⫺.027 0 0

.377 ⫺.126 0 0

.203 0 0

.086 .037

.042

Note. Diagonals in lower part of Table 3 are variances and covariances in off diagonals. Covariances across traits and methods are constrained to zero. SOC ⫽ first order Social Pros; PC ⫽ computer questionnaire (numbers ⫽ time points); Paper ⫽ paper questionnaire (numbers ⫽ time points); COP ⫽ first order Coping Pros; HEAL ⫽ first order Health Cons.

described by Campbell and Fisk (1959), high correlations are evidence against discriminant validity. However, CFA indicates that the Social and Coping Pros are distinct trait factors (Plummer et al., 2001). The lack of precision and the subjective judgment inherent in the traditional MTMM framework make it difficult to apply to situations where there are high correlations between traits. Applying HCFA MTMM as we did confirms the distinctiveness of the Social and Coping Pros. One concern in our approach arises from the longitudinal nature of the data. One approach to this is to allow correlations between the same items from same type of questionnaire across adjacent measurement occasions. This approach is equivalent to measurement invariance testing across measurement occasions. However, fitting a measurement invariance model within an HCFA MTMM structure resulted in the model not being identified. This is expected. In MTMM analysis, large sample sizes and an MTMM design larger than the minimal three-trait three-method matrix have been recommended to avoid convergent and inadmissible solution problems (Lance et al., 2002). Marsh and Hocevar (1983) suggested setting the error term variance to a predetermined value based on the observed data to attain a stable result in a study that only had two methods. However, they recommended a minimum of three traits and three methods. In our study, with three traits and two methods, this was insufficient for a single MTMM analysis. However, in Guo, Aveyard, Fielding, and Sutton (in press), we found measurement invariance across occasions, suggesting that order effects would not be distorting our results. Other authors have also struggled with this. For example, Metzler, Biglan, Ary, and Li (1998) treated measurement occasion as a method factor (Metzler et al., 1998). We treated each measurement occasion as a separate test, which led to the model being identified. This approach models the correlation of first order factors between measurement occasions as second order method or trait factors. It does not allow direct estimation of the correlations between first factors

Table 4 Factor Loading of Computer Questionnaire Items on the First Order Factor Item Q1. Smoking makes people get more respect from others. Q3. Teenagers who smoke have more friends. Q11. Teenagers who smoke have more boy/girlfriends. Q5. Smoking helps people to cope better with frustrations. Q7. Smoking cigarettes is pleasurable. Q9. Smoking cigarettes relieves tension. Q4. Smoking can affect the health of others. Q6. Smoking cigarettes is hazardous to people’s health. Q8. Cigarette smoke bothers other people.

SOC PC1

COP PC1

HEAL PC1

SOC PC2

COP PC2

HEAL PC2

SOC PC3

.697

.708

.794

.773

.772

.858

.695

.742

.808

COP PC3

.790 .724

.805 .753

.846 .766

.847

.837

.866

HEAL PC3

.694

.791

.803

.696

.719

.814

.684

.683

.741

Note. SOC ⫽ first order Social Pros; PC ⫽ computer questionnaire (numbers ⫽ time points); COP ⫽ first order Coping Pros; HEAL ⫽ first order Health Cons.

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Table 5 Factor Loading of Paper Questionnaire Items on the First Order Factor Item Q2. Young people who smoke have more friends. Q5. Young people who smoke go out on more dates. Q8. Young people who smoke get more respect from others. Q1. Smoking helps people to cope better with frustrations. Q4. Smoking cigarettes relieves tension. Q6. Smoking cigarettes is pleasurable. Q3. Smoking cigarettes is hazardous to people’s health. Q7. Smoking can affect the health of others. Q9. Cigarette smoke bothers other people.

SOC Paper1

COP Paper1

HEAL Paper1

SOC Paper2

COP Paper2

HEAL Paper2

SOC Paper3

.701

.798

.834

.650

.754

.771

.658

.818

.833

COP Paper3

.733

.842

.878

.748

.881

.903

.579

.689

.664

HEAL Paper3

.538

.665

.667

.654

.771

.809

.611

.708

.699

Note. SOC ⫽ first order Social Pros; Paper ⫽ paper questionnaire (numbers ⫽ time points); COP ⫽ first order Coping Pros; HEAL ⫽ first order Health Cons.

in second order CFA, but as this is not the focus of CFA MTMM analysis, this is not a major concern. Although the convergent and discriminant validity of the Decisional Balance Scale are supported, results on the HCFA MTMM CTCM model have loadings on both second order Paper and Computer method factors that are statistically significant. The second order method factor variances are also statistically significant. This indicates that the undesirable influence of a particular method biases the responses given and inflates the correlation among the different traits measured with the same method. In this study, there are two possible reasons, which are impossible to distinguish. The first is that response formats to the scales varied, agreement in one and importance in the other. A second possibility is what is termed the method halo effect (Marsh & Grayson, 1992), meaning that people give responses to a computerized questionnaire that they would not give to the paper version. It would of course have been preferable to have had the same response format to both questionnaires. This is potentially of importance because these questionnaires have been incorporated, as in our study, into computerized interventions. Knowing whether there are true method factor effects or not would be important in understanding the effects of these interventions on smoking status, particularly if we are able to examine mediation by decisional balance. Taking all studies of decisional balance for smoking in adolescence together, they consistently point to either a three-factor (Pallonen et al., 1998; Plummer et al., 2001) or, in our unpublished manuscript, a four-factor solution, and not the simple two-factor solution found so consistently in adults (Prochaska et al., 1994). These results indicate good factorial validity. Taken together, studies seem to indicate that response format seems to matter much less than might be supposed. Construct validity is indicated by the convergent and discriminant validity demonstrated here. Some evidence of concurrent validity is shown in cross-sectional data demonstrating differences in mean scores between stages for the

pros and cons (Plummer et al., 2001). Bearing in mind the strong and weak principles of change, the key construct that needs to be demonstrated is predictive ability. Those with higher scores in cons and lower scores in pros should be more likely to move stage and hence stop smoking. A match/mismatch trial showed some evidence in adults that interventions affecting pros and cons had different effects in different stages, as predicted in a variant of the TTM (Dijkstra et al., 2006). The key task, therefore, in future research, is to test the predictions of the TTM, that pros and cons cause stage movement.

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Received February 28, 2007 Revision received July 23, 2007 Accepted August 5, 2007 䡲