Journal of Personality Assessment, 97(2), 191–199, 2015 Copyright Ó Taylor & Francis Group, LLC ISSN: 0022-3891 print / 1532-7752 online DOI: 10.1080/00223891.2014.938158
Evaluation of the Bifactor Structure of the Dispositional Hope Scale RAPSON GOMEZ, SUZANNE MCLAREN, MERSEY SHARP, CARA SMITH, KATE HEARN, AND LEAH TURNER School of Health Sciences, University of Ballarat, Australia The Dispositional Hope Scale (DHS; Snyder et al., 1991) is composed of items assessing an individual’s perception of his or her agency and pathways. This study examined support for the bifactor structure and relation of the factors in this model with depressive symptoms. It also examined cross-gender measurement invariance for the bifactor model. A community sample of 413 women and 257 men completed the DHS. Confirmatory factor analysis indicated more support for the bifactor model than the 1- and 2-factor models. Results also indicated full measurement invariance across gender for the bifactor and the 2-factor models. The general and the specific agency factors, but not the specific pathways factor, correlated with depressive symptoms. The better support for the bifactor model suggests that ideally hope has to be measured and examined by factors reflecting high covariance for agency and pathways, and also factors reflecting unique variances for agency and pathways. The support for full cross-gender measurement invariance indicated that there are no differences in measurement and scaling properties for the DHS across ratings provided by women and men, and therefore the DHS ratings can be scored in the same way for women and men.
A major model of hope is that proposed by Snyder et al. (1991; see also Snyder, 2000). According to Snyder et al., hope is “a reciprocally derived sense of successful agency (goal-directed determination) and pathways (planning of ways to meet the goals)” (p. 571). Studies that have examined this model have used the Dispositional Hope Scale (DHS; Snyder et al., 1991). Most studies of the factor structure of the DHS have supported a two-factor model (factors for agency and pathways), with very high correlation between the factors. This has been interpreted as supportive of the hope model proposed by Snyder et al. To date, at least one study has reported support for a bifactor model (Brouwer, Meijer, Weekers, & Baneke, 2008), comprising a general hope factor and specific factors for agency and pathways. This study provided a more detailed evaluation of this bifactor model, and thereby an opportunity for refinement and extension of Snyder et al.’s hope model. In the hope model proposed by Snyder et al. (1991), pathways is a cognitive component of hope, and it refers to planning ways to meet goals or one’s belief about the capacity to generate routes to reach goals. Individuals with high pathways are considered to be able to generate multiple routes for attaining goals. Agency is a motivational component of hope, and it refers to goal-directed determination or one’s belief about the capacity to initiate and sustain actions toward goals. Individuals with high agency are thought to have the ability to move effectively along the selected pathways. Agency is seen as the driving force for hope. According to Snyder et al., although agency and pathways are not synonymous, neither one by itself is sufficient to experience hope. Hope requires the activation of both agency and pathways together. The DHS that has been used to study Snyder et al.’s (1991) hope model is a self-report measure that has 12 items, of which 8 items cover hope and 4 items are fillers (with no
Received January 10, 2013; Revised May 25, 2014. Address correspondence to Rapson Gomez, School of Health Sciences, University of Ballarat, PO Box 663, Ballarat VIC 3353, Australia; E-mail: [email protected]
relevance to hope). Four of the 8 hope items cover agency and the other 4 items cover pathways. The initial development and validation study of the DHS involved six college student samples and two psychological treatment samples (Snyder et al., 1991). Principal components analysis (PCA) indicated support for two correlated factors. One factor included the four agency items, and the other factor included the four pathways items (see Figure 1, left side). As these factors had moderately high correlations, ranging from .39 to .57, Snyder et al. argued that the agency and pathways components, although not synonymous, are closely related and function together. Confirmatory factor analysis (CFA) has also been used to examine the factor structure of the DHS (e.g., Babyak, Snyder, & Yoshinobu, 1993; Qiwu, Kok, & Chuang, 2012; Roesch & Vaughn, 2006). These studies involving mainly undergraduate students (Qiwu et al. also examined college academic advisors) have generally reported acceptable fit for the two-factor model, with this model showing better fit than a one-factor model (with all items loading on a single factor). Babyak et al. also reported support for a second-order factor model in which the agency and pathways factors loaded on a single higher order general hope factor. However, the latter finding is questionable, as a single higher order factor cannot be specified with only two primary factors, and as such a model will be underidentified (Brown, 2006). A consistent finding in virtually all past CFA studies is the very high correlation between the agency and pathways latent factors. For example, Roesch and Vaughn reported a correlation of .82. A study by Brouwer et al. (2008) involving psychiatric patients, delinquents, and students reported a correlation of .91. The high correlation can be interpreted as consistent with a higher order hope factor. Given this and Snyder et al.’s (1991) hope model, with few exceptions, most studies have used the total DHS score for studying hope. Although Snyder et al. (1991) and other researchers have viewed the total hope score as representing the higher order DHS hope factor, we argue that this practice might be psychometrically problematic. As the total score is the sum of all the eight agency and pathways items, it comprises the shared variance across all agency and pathways items, as
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P1
P1
P4
P4
P6
Pathways
P8
General
A2 A9 A10 A12
Agency
Pathways
P6 P8 A2 A9 A10
Agency
A12
FIGURE 1.—Schematic path diagram of the two-factor oblique (left) and bifactor (right) models. Note. P D pathways; A D agency.
well as the unique variance within the agency items and the unique variance within the pathways items. In contrast, the higher order hope factor (that has been linked to hope in the Snyder et al. model), is only the shared variance of the agency and pathways primary factors. Thus the total DHS score is not the same as the score for the higher order factor. This means that the findings from past studies that have used the total DHS score have not used a score that reflects the hope construct as depicted in the Snyder et al. hope theory. Also, by using the total score, past studies have overlooked the possibility of unique contributions by the agency and pathways components to hope and to relevant other external variables (Chang, 2003). Using the total hope score, studies have shown that low hope is associated with poor adjustment, such as high negative affect (Snyder et al., 1991), depressive symptoms among college students (Chang, 2003), and burnout among nurses (Sherwin et al., 1992). The findings from a handful of studies have raised the possibility that both agency and pathways contribute uniquely to how hope is related to relevant external variables. A longitudinal study by Arnau, Rosen, Finch, Rhudy, and Fortunato (2007) that involved college students and the application of cross-lagged panel models found that agency, but not pathways, contributed uniquely to the predictions of later depression and anxiety symptoms. The researchers, however, raised the possibility that the shared variance for agency and pathways, rather than the unique variances in them, could have contributed to these findings. This is because in crosslagged panel models involving two latent predictors, only one latent variable will show a significant effect if the shared variance between it and another latent variable contributes to the significant prediction. The recent study by Qiwu et al. (2012) found that agency, but not pathways, uniquely predicted general well-being (in a group of undergraduate students) and job burnout (in a group of academic advisors). Taken together, the findings in these studies suggest differential associations for agency and pathways factors with relevant external variables. More important, they show that agency, but not pathways, is linked to relevant external correlates, which is inconsistent with the hope model proposed by Snyder et al. (1991). The findings also highlight that the examination of the agency and pathways components as separate hope constructs would be valuable in extending and refining hope theory. Although dominance analysis (Budescu, 1993) or residualized relative importance analysis (LeBreton, Tonidandel, & Krasikova, 2013) can provide a test of the relative importance of the agency and pathways components in predicting external
correlates, they do not enable a complete evaluation of Snyder et al.’s model, as it would be necessary to also include the overall latent factor in some way. Representation of the overall hope factor (to reflect Snyder et al.’s [1991] hope theory) and the specific factors for agency and pathways, after controlling for the effects of the overall hope factor (to allow an examination of the unique contributions of agency and pathways), is possible using the CFA bifactor model framework. A bifactor model is a simple orthogonal model with a general factor on which all items load, and two or more specific factors (unique factors). The general factor represents covariance among all the items, whereas the specific factors represent domain-specific item response covariances, not accounted for by the general factor. The bifactor model is different from a conventional secondorder factor model. In a second-order factor model, the higher order factor explains the covariance of the primary factors, and not the items, as is the case of the general factor in a bifactor model (Reise, Moore, & Haviland, 2010). Although the second-order factor and the disturbances of the first-order factors in the second-order model correspond to the general factor and the unique factors of the bifactor model, the bifactor model has the advantage over the second-order factor model in that it allows evaluation of the relations between items and specific factors, after controlling for the general factor. This is not possible in the second-order model. Another advantage is that as the general and specific factors are independent factors, it can examine the relation among all these factors and relevant external variables. In contrast, this is not possible in a second-order factor model, as the proportionality constraint (equating the ratio of variance attributable to the first-order factor to variance attributable to the general factor) inherent in this model will mean that the regression path of at least one factor to the external variable is fixed at zero for identification (Reise et al., 2010). Figure 1 (right side) shows a conceptual path diagram of the bifactor model as applied to the DHS. As shown, it is a confirmatory (restricted) factor model with three orthogonal factors: a general factor on which all eight hope items load, and specific factors for the agency and pathways items. The general factor explains the covariance across all the agency and pathways items, whereas the specific factors explain the unique variance of the items within the specific factors, after controlling for the variance in the general factor. This means that with the bifactor model, it will be possible to ascertain the extent to which items in the DHS capture the variance for the general hope factor and the unique variance for agency and pathways after removing the variance for the general hope factor. Thus, the bifactor conceptualization of the DHS would allow us to concurrently model the overall or general latent factor for hope, and also the specific components of agency and pathways that are independent of each other and the general hope factor. The application of such a model would, therefore, enable not only a more accurate evaluation of Snyder et al.’s (1991) hope model, but also a refinement of this model. To date, only the study by Brouwer et al. (2008) has examined a bifactor conceptualization of the DHS. As noted previously, this study examined samples of psychiatric patients, delinquents, and students. For all three samples together and for the psychiatric patient and student groups separately, the study found support for the bifactor model. The bifactor model
DISPOSITIONAL HOPE SCALE was not applied to the delinquent group because of the small sample size. For this model, the factor loadings were higher for the general factor than the specific factors. In view of these findings, Brouwer et al. suggested that there was no justification for treating the agency and pathways items as separate. Using Thurstone’s (1947) classical criterion for “salience” as standardized factor loading being >.30, an examination of the bifactor models shows that there were a number of items with salient loadings on the specific factors. For the sample as a whole, there was one agency item (Item 2) and two pathways items (Items 1 and 4). For the psychiatric patients, there was one agency item (Item 2), and three pathways items (Items 1, 4, and 8). Thus, for at least some of the DHS items, in particular the pathways items, there were salient amounts of unique variance that should not be ignored. Thus, we believe there is merit in examining the separate contributions of the unique agency and unique pathways components of hope. As added support for our view that we continue to examine the role of the unique agency and unique pathways components, we argue that the specific factors should not be ignored unless it can be demonstrated that they have no relations with meaningful external variables. If this can be demonstrated consistently, then it could imply that the unique variance for agency and pathways, even if substantial, have little predictive value over that of a general hope factor and are, therefore, of no practical value. In contrast, if this is not demonstrated consistently, then it could imply that the unique variances for agency and pathways have important additional general predictive values, and are therefore of value. As the study by Brouwer et al. (2008) did not examine how the general and specific factors were related to relevant external variables, we do not have such data, and this remains an empirical question worthy of future research. Like other CFA models, the CFA bifactor model can also be evaluated for measurement invariance. Measurement invariance refers to groups reporting the same observed scores when they have the same level of the underlying trait (Reise, Widaman, & Paugh, 1993). When groups are compared or distinguished using a questionnaire, measurement invariance for scores in that questionnaire across the groups is a prerequisite. Invariance would mean that for the groups being compared, the questionnaire is using the same measurement and scaling properties. If there is weak or no support for invariance, then it follows that the groups in question cannot be justifiably compared in terms of observed scores of the questionnaire, as the same observed score for the groups does not reflect the same level of the underlying trait. Expressed differently, the scores are functioning differently across the groups. A powerful method for examining measurement invariance is the multiple-group mean and covariance structures CFA approach. Assuming that the indicator ratings are treated as ordered-categorical (as in the DHS), this approach can test for configural invariance (same overall factor structure), metric invariance or item factor loadings invariance (same strength of the associations of items with the first-order factors), and invariance for thresholds or equivalency for responses for the different item categories rather than intercept invariance is a more useful test. To date, at least two studies have used CFA models to examine various levels of invariance for the DHS across gender (Babyak et al., 1993; Roesch & Vaughn, 2006). Both
193 studies used the two-factor model. As noted previously, the study by Babyak et al. examined four different college student samples. They found noninvariance for the factor loadings of some items in two samples, with one sample having higher loadings for agency in men, and another sample having higher loadings for agency in women. Using the two-factor model, Roesch and Vaughn’s study involving college students found support for configural (same form) and metric (same factor loadings) invariance. However, there was lack of support for full invariance for intercepts. More specifically, men scored higher intercepts for three pathways items (Items 1, 4, and 8), and for one agency item (Item 10). These findings suggest that men and women interpret and respond differently to some of the DHS items. These findings would appear to suggest that some DHS items could lack measurement invariance even when they are modeled within a bifactor framework. However, as this has not been empirically tested, this remains an area worthy of future research. Indeed, if it can be shown that there is support for full measurement invariance for the DHS bifactor model across men and women, it could add further support for the robustness of this model. In summary, existing data suggest support for the two-factor and bifactor models for the DHS. For the two-factor model, support has been found for full measurement invariance for the configural (same form) and metric (same factor loadings) invariance models. There has been partial support for intercepts. Studies have also shown the agency and pathways components (based on subscale scores) to have different associations with relevant outcome variables, such as depressive symptoms. Despite such findings, we argue that there are limitations in existing data for the DHS. First, virtually all studies that have examined the structural model of the DHS have used student samples, or other specific samples and not general community samples (e.g., college student and psychological treatment samples in the study by Snyder et al., 1991; college student sample in the studies by Babyak et al., 1993; Roesch & Vaughn, 2006; and Arnau et al., 2007; college academic advisor and undergraduate student samples in the study by Qiwu et al., 2012). The only study that has examined the bifactor model of the DHS has used samples of psychiatric patients, delinquents, and students (Brouwer et al., 2008). This practice can be seen as limiting, as their responses are unlikely to adequately represent the entire trait spectrum for hope. Second, despite showing most support for the bifactor model, there are no data on how the factors in this model are associated with relevant external variables. There are also no data on measurement invariance of the bifactor model across men and women. The limitations discussed suggest that there is a need for more studies of the structure of the DHS focusing on general community samples, and that it would be valuable for such studies to examine support for the internal structure of the bifactor model, and to explore how the factors in this model are associated with relevant external variables. Additionally, it would be useful for future studies to explore measurement invariance of the bifactor model across men and women. Support for the bifactor model can be inferred if there is good fit for the bifactor model, with substantial factor loadings for the general factor, and for the agency or pathways-specific factors. In addition, it will be necessary for both the general hope
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factor, and for the agency or pathways-specific factors, to predict depressive symptoms. The overall aim of this study was to use CFA procedures to examine if there is support for a bifactor conceptualization of the DHS. We first attempted to replicate the bifactor model of the DHS reported by Brouwer et al. (2008). As a further test of the validity of the bifactor model, we used a structural equation modeling (SEM) procedure to examine how the general and specific factors in the bifactor model were related to depressive symptoms. In this respect previous studies have shown that hope is associated negatively with depressive symptoms (Arnau et al., 2007; Chang, 2003; Chang & DeSimone, 2001). For comparison, the study also tested the fit of the two-factor oblique model and the one-factor model, and the associations of the factors in these models with depressive symptoms. We also test gender invariance for the two-factor model. Based on previous findings involving the two-factor model (Babyak et al., 1993; Roesch & Vaughn, 2006, reviewed earlier), we expected support for metric and threshold invariances for most, but not all items.
METHOD Participants The sample included 670 adults, 413 women and 257 men, from 18 to 65 years old. All participants were from the general community. The mean age of all participants was 35.25 years (SD D 14.15). The mean age of women (M D 34.33, SD D 13.72) and men (M D 36.72, SD D 14.68) differed significantly, t(668) D 2.13, p
Evaluation of the Bifactor Structure of the Dispositional Hope Scale RAPSON GOMEZ, SUZANNE MCLAREN, MERSEY SHARP, CARA SMITH, KATE HEARN, AND LEAH TURNER School of Health Sciences, University of Ballarat, Australia The Dispositional Hope Scale (DHS; Snyder et al., 1991) is composed of items assessing an individual’s perception of his or her agency and pathways. This study examined support for the bifactor structure and relation of the factors in this model with depressive symptoms. It also examined cross-gender measurement invariance for the bifactor model. A community sample of 413 women and 257 men completed the DHS. Confirmatory factor analysis indicated more support for the bifactor model than the 1- and 2-factor models. Results also indicated full measurement invariance across gender for the bifactor and the 2-factor models. The general and the specific agency factors, but not the specific pathways factor, correlated with depressive symptoms. The better support for the bifactor model suggests that ideally hope has to be measured and examined by factors reflecting high covariance for agency and pathways, and also factors reflecting unique variances for agency and pathways. The support for full cross-gender measurement invariance indicated that there are no differences in measurement and scaling properties for the DHS across ratings provided by women and men, and therefore the DHS ratings can be scored in the same way for women and men.
A major model of hope is that proposed by Snyder et al. (1991; see also Snyder, 2000). According to Snyder et al., hope is “a reciprocally derived sense of successful agency (goal-directed determination) and pathways (planning of ways to meet the goals)” (p. 571). Studies that have examined this model have used the Dispositional Hope Scale (DHS; Snyder et al., 1991). Most studies of the factor structure of the DHS have supported a two-factor model (factors for agency and pathways), with very high correlation between the factors. This has been interpreted as supportive of the hope model proposed by Snyder et al. To date, at least one study has reported support for a bifactor model (Brouwer, Meijer, Weekers, & Baneke, 2008), comprising a general hope factor and specific factors for agency and pathways. This study provided a more detailed evaluation of this bifactor model, and thereby an opportunity for refinement and extension of Snyder et al.’s hope model. In the hope model proposed by Snyder et al. (1991), pathways is a cognitive component of hope, and it refers to planning ways to meet goals or one’s belief about the capacity to generate routes to reach goals. Individuals with high pathways are considered to be able to generate multiple routes for attaining goals. Agency is a motivational component of hope, and it refers to goal-directed determination or one’s belief about the capacity to initiate and sustain actions toward goals. Individuals with high agency are thought to have the ability to move effectively along the selected pathways. Agency is seen as the driving force for hope. According to Snyder et al., although agency and pathways are not synonymous, neither one by itself is sufficient to experience hope. Hope requires the activation of both agency and pathways together. The DHS that has been used to study Snyder et al.’s (1991) hope model is a self-report measure that has 12 items, of which 8 items cover hope and 4 items are fillers (with no
Received January 10, 2013; Revised May 25, 2014. Address correspondence to Rapson Gomez, School of Health Sciences, University of Ballarat, PO Box 663, Ballarat VIC 3353, Australia; E-mail: [email protected]
relevance to hope). Four of the 8 hope items cover agency and the other 4 items cover pathways. The initial development and validation study of the DHS involved six college student samples and two psychological treatment samples (Snyder et al., 1991). Principal components analysis (PCA) indicated support for two correlated factors. One factor included the four agency items, and the other factor included the four pathways items (see Figure 1, left side). As these factors had moderately high correlations, ranging from .39 to .57, Snyder et al. argued that the agency and pathways components, although not synonymous, are closely related and function together. Confirmatory factor analysis (CFA) has also been used to examine the factor structure of the DHS (e.g., Babyak, Snyder, & Yoshinobu, 1993; Qiwu, Kok, & Chuang, 2012; Roesch & Vaughn, 2006). These studies involving mainly undergraduate students (Qiwu et al. also examined college academic advisors) have generally reported acceptable fit for the two-factor model, with this model showing better fit than a one-factor model (with all items loading on a single factor). Babyak et al. also reported support for a second-order factor model in which the agency and pathways factors loaded on a single higher order general hope factor. However, the latter finding is questionable, as a single higher order factor cannot be specified with only two primary factors, and as such a model will be underidentified (Brown, 2006). A consistent finding in virtually all past CFA studies is the very high correlation between the agency and pathways latent factors. For example, Roesch and Vaughn reported a correlation of .82. A study by Brouwer et al. (2008) involving psychiatric patients, delinquents, and students reported a correlation of .91. The high correlation can be interpreted as consistent with a higher order hope factor. Given this and Snyder et al.’s (1991) hope model, with few exceptions, most studies have used the total DHS score for studying hope. Although Snyder et al. (1991) and other researchers have viewed the total hope score as representing the higher order DHS hope factor, we argue that this practice might be psychometrically problematic. As the total score is the sum of all the eight agency and pathways items, it comprises the shared variance across all agency and pathways items, as
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P1
P1
P4
P4
P6
Pathways
P8
General
A2 A9 A10 A12
Agency
Pathways
P6 P8 A2 A9 A10
Agency
A12
FIGURE 1.—Schematic path diagram of the two-factor oblique (left) and bifactor (right) models. Note. P D pathways; A D agency.
well as the unique variance within the agency items and the unique variance within the pathways items. In contrast, the higher order hope factor (that has been linked to hope in the Snyder et al. model), is only the shared variance of the agency and pathways primary factors. Thus the total DHS score is not the same as the score for the higher order factor. This means that the findings from past studies that have used the total DHS score have not used a score that reflects the hope construct as depicted in the Snyder et al. hope theory. Also, by using the total score, past studies have overlooked the possibility of unique contributions by the agency and pathways components to hope and to relevant other external variables (Chang, 2003). Using the total hope score, studies have shown that low hope is associated with poor adjustment, such as high negative affect (Snyder et al., 1991), depressive symptoms among college students (Chang, 2003), and burnout among nurses (Sherwin et al., 1992). The findings from a handful of studies have raised the possibility that both agency and pathways contribute uniquely to how hope is related to relevant external variables. A longitudinal study by Arnau, Rosen, Finch, Rhudy, and Fortunato (2007) that involved college students and the application of cross-lagged panel models found that agency, but not pathways, contributed uniquely to the predictions of later depression and anxiety symptoms. The researchers, however, raised the possibility that the shared variance for agency and pathways, rather than the unique variances in them, could have contributed to these findings. This is because in crosslagged panel models involving two latent predictors, only one latent variable will show a significant effect if the shared variance between it and another latent variable contributes to the significant prediction. The recent study by Qiwu et al. (2012) found that agency, but not pathways, uniquely predicted general well-being (in a group of undergraduate students) and job burnout (in a group of academic advisors). Taken together, the findings in these studies suggest differential associations for agency and pathways factors with relevant external variables. More important, they show that agency, but not pathways, is linked to relevant external correlates, which is inconsistent with the hope model proposed by Snyder et al. (1991). The findings also highlight that the examination of the agency and pathways components as separate hope constructs would be valuable in extending and refining hope theory. Although dominance analysis (Budescu, 1993) or residualized relative importance analysis (LeBreton, Tonidandel, & Krasikova, 2013) can provide a test of the relative importance of the agency and pathways components in predicting external
correlates, they do not enable a complete evaluation of Snyder et al.’s model, as it would be necessary to also include the overall latent factor in some way. Representation of the overall hope factor (to reflect Snyder et al.’s [1991] hope theory) and the specific factors for agency and pathways, after controlling for the effects of the overall hope factor (to allow an examination of the unique contributions of agency and pathways), is possible using the CFA bifactor model framework. A bifactor model is a simple orthogonal model with a general factor on which all items load, and two or more specific factors (unique factors). The general factor represents covariance among all the items, whereas the specific factors represent domain-specific item response covariances, not accounted for by the general factor. The bifactor model is different from a conventional secondorder factor model. In a second-order factor model, the higher order factor explains the covariance of the primary factors, and not the items, as is the case of the general factor in a bifactor model (Reise, Moore, & Haviland, 2010). Although the second-order factor and the disturbances of the first-order factors in the second-order model correspond to the general factor and the unique factors of the bifactor model, the bifactor model has the advantage over the second-order factor model in that it allows evaluation of the relations between items and specific factors, after controlling for the general factor. This is not possible in the second-order model. Another advantage is that as the general and specific factors are independent factors, it can examine the relation among all these factors and relevant external variables. In contrast, this is not possible in a second-order factor model, as the proportionality constraint (equating the ratio of variance attributable to the first-order factor to variance attributable to the general factor) inherent in this model will mean that the regression path of at least one factor to the external variable is fixed at zero for identification (Reise et al., 2010). Figure 1 (right side) shows a conceptual path diagram of the bifactor model as applied to the DHS. As shown, it is a confirmatory (restricted) factor model with three orthogonal factors: a general factor on which all eight hope items load, and specific factors for the agency and pathways items. The general factor explains the covariance across all the agency and pathways items, whereas the specific factors explain the unique variance of the items within the specific factors, after controlling for the variance in the general factor. This means that with the bifactor model, it will be possible to ascertain the extent to which items in the DHS capture the variance for the general hope factor and the unique variance for agency and pathways after removing the variance for the general hope factor. Thus, the bifactor conceptualization of the DHS would allow us to concurrently model the overall or general latent factor for hope, and also the specific components of agency and pathways that are independent of each other and the general hope factor. The application of such a model would, therefore, enable not only a more accurate evaluation of Snyder et al.’s (1991) hope model, but also a refinement of this model. To date, only the study by Brouwer et al. (2008) has examined a bifactor conceptualization of the DHS. As noted previously, this study examined samples of psychiatric patients, delinquents, and students. For all three samples together and for the psychiatric patient and student groups separately, the study found support for the bifactor model. The bifactor model
DISPOSITIONAL HOPE SCALE was not applied to the delinquent group because of the small sample size. For this model, the factor loadings were higher for the general factor than the specific factors. In view of these findings, Brouwer et al. suggested that there was no justification for treating the agency and pathways items as separate. Using Thurstone’s (1947) classical criterion for “salience” as standardized factor loading being >.30, an examination of the bifactor models shows that there were a number of items with salient loadings on the specific factors. For the sample as a whole, there was one agency item (Item 2) and two pathways items (Items 1 and 4). For the psychiatric patients, there was one agency item (Item 2), and three pathways items (Items 1, 4, and 8). Thus, for at least some of the DHS items, in particular the pathways items, there were salient amounts of unique variance that should not be ignored. Thus, we believe there is merit in examining the separate contributions of the unique agency and unique pathways components of hope. As added support for our view that we continue to examine the role of the unique agency and unique pathways components, we argue that the specific factors should not be ignored unless it can be demonstrated that they have no relations with meaningful external variables. If this can be demonstrated consistently, then it could imply that the unique variance for agency and pathways, even if substantial, have little predictive value over that of a general hope factor and are, therefore, of no practical value. In contrast, if this is not demonstrated consistently, then it could imply that the unique variances for agency and pathways have important additional general predictive values, and are therefore of value. As the study by Brouwer et al. (2008) did not examine how the general and specific factors were related to relevant external variables, we do not have such data, and this remains an empirical question worthy of future research. Like other CFA models, the CFA bifactor model can also be evaluated for measurement invariance. Measurement invariance refers to groups reporting the same observed scores when they have the same level of the underlying trait (Reise, Widaman, & Paugh, 1993). When groups are compared or distinguished using a questionnaire, measurement invariance for scores in that questionnaire across the groups is a prerequisite. Invariance would mean that for the groups being compared, the questionnaire is using the same measurement and scaling properties. If there is weak or no support for invariance, then it follows that the groups in question cannot be justifiably compared in terms of observed scores of the questionnaire, as the same observed score for the groups does not reflect the same level of the underlying trait. Expressed differently, the scores are functioning differently across the groups. A powerful method for examining measurement invariance is the multiple-group mean and covariance structures CFA approach. Assuming that the indicator ratings are treated as ordered-categorical (as in the DHS), this approach can test for configural invariance (same overall factor structure), metric invariance or item factor loadings invariance (same strength of the associations of items with the first-order factors), and invariance for thresholds or equivalency for responses for the different item categories rather than intercept invariance is a more useful test. To date, at least two studies have used CFA models to examine various levels of invariance for the DHS across gender (Babyak et al., 1993; Roesch & Vaughn, 2006). Both
193 studies used the two-factor model. As noted previously, the study by Babyak et al. examined four different college student samples. They found noninvariance for the factor loadings of some items in two samples, with one sample having higher loadings for agency in men, and another sample having higher loadings for agency in women. Using the two-factor model, Roesch and Vaughn’s study involving college students found support for configural (same form) and metric (same factor loadings) invariance. However, there was lack of support for full invariance for intercepts. More specifically, men scored higher intercepts for three pathways items (Items 1, 4, and 8), and for one agency item (Item 10). These findings suggest that men and women interpret and respond differently to some of the DHS items. These findings would appear to suggest that some DHS items could lack measurement invariance even when they are modeled within a bifactor framework. However, as this has not been empirically tested, this remains an area worthy of future research. Indeed, if it can be shown that there is support for full measurement invariance for the DHS bifactor model across men and women, it could add further support for the robustness of this model. In summary, existing data suggest support for the two-factor and bifactor models for the DHS. For the two-factor model, support has been found for full measurement invariance for the configural (same form) and metric (same factor loadings) invariance models. There has been partial support for intercepts. Studies have also shown the agency and pathways components (based on subscale scores) to have different associations with relevant outcome variables, such as depressive symptoms. Despite such findings, we argue that there are limitations in existing data for the DHS. First, virtually all studies that have examined the structural model of the DHS have used student samples, or other specific samples and not general community samples (e.g., college student and psychological treatment samples in the study by Snyder et al., 1991; college student sample in the studies by Babyak et al., 1993; Roesch & Vaughn, 2006; and Arnau et al., 2007; college academic advisor and undergraduate student samples in the study by Qiwu et al., 2012). The only study that has examined the bifactor model of the DHS has used samples of psychiatric patients, delinquents, and students (Brouwer et al., 2008). This practice can be seen as limiting, as their responses are unlikely to adequately represent the entire trait spectrum for hope. Second, despite showing most support for the bifactor model, there are no data on how the factors in this model are associated with relevant external variables. There are also no data on measurement invariance of the bifactor model across men and women. The limitations discussed suggest that there is a need for more studies of the structure of the DHS focusing on general community samples, and that it would be valuable for such studies to examine support for the internal structure of the bifactor model, and to explore how the factors in this model are associated with relevant external variables. Additionally, it would be useful for future studies to explore measurement invariance of the bifactor model across men and women. Support for the bifactor model can be inferred if there is good fit for the bifactor model, with substantial factor loadings for the general factor, and for the agency or pathways-specific factors. In addition, it will be necessary for both the general hope
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factor, and for the agency or pathways-specific factors, to predict depressive symptoms. The overall aim of this study was to use CFA procedures to examine if there is support for a bifactor conceptualization of the DHS. We first attempted to replicate the bifactor model of the DHS reported by Brouwer et al. (2008). As a further test of the validity of the bifactor model, we used a structural equation modeling (SEM) procedure to examine how the general and specific factors in the bifactor model were related to depressive symptoms. In this respect previous studies have shown that hope is associated negatively with depressive symptoms (Arnau et al., 2007; Chang, 2003; Chang & DeSimone, 2001). For comparison, the study also tested the fit of the two-factor oblique model and the one-factor model, and the associations of the factors in these models with depressive symptoms. We also test gender invariance for the two-factor model. Based on previous findings involving the two-factor model (Babyak et al., 1993; Roesch & Vaughn, 2006, reviewed earlier), we expected support for metric and threshold invariances for most, but not all items.
METHOD Participants The sample included 670 adults, 413 women and 257 men, from 18 to 65 years old. All participants were from the general community. The mean age of all participants was 35.25 years (SD D 14.15). The mean age of women (M D 34.33, SD D 13.72) and men (M D 36.72, SD D 14.68) differed significantly, t(668) D 2.13, p
