The State-Trait Model of Cheerfulness: Tests of Measurement Invariance and Latent Mean Differences in European and Chinese Canadian Students

The State-Trait Cheerfulness Inventory (STCI) assesses latent traits and states of cheerfulness, seriousness, and bad mood to represent the temperamental basis of humor. The present study (1) tested the generalizability of the three-factor model in both state and trait versions of the STCI across European Canadian (N = 489) and first generation Chinese Canadian (N = 147) participants completing the English version of the STCI and (2) compared latent mean differences. Results indicated the confirmatory factor analyses of the three-factor model for European White participants born in Canada and Chinese participants born in China showed adequate fit for both trait and state measures. Furthermore, substantial equivalence of factor model parameters and partial scalar invariance were found for both the state and trait STCI measures. In examining latent mean differences, European White Canadian participants reported significantly higher trait cheerfulness, z = 3.30, p < .001, d = 0.84, and lower trait bad mood z = 3.25, p < .01, d = 0.80 compared to the Chinese Canadian groups. European White Canadian participants reported significantly lower state bad mood, z = 3.59, p < .001, d = 1.15, compared to the Chinese Canadian groups. Limitations and future directions based on study findings are discussed.


Objectives
The aim of the present study was to test (1) the generalizability of the three-factor model in both state and trait versions of the state-trait model of cheerfulness across European Canadian and Chinese Canadian participants completing the English version of the STCI and (2) to compare latent mean differences. Measurement invariance analyses of the temperamental basis of humor can provide a solid foundation in ruling out measurement artifacts when interpreting findings for future cross-cultural studies that utilize the STCI.

Method Participants and Procedure
Undergraduate students who are enrolled with English as their primary language from a large Canadian university were invited to participate in the study. Upon signing up for the study, participants were instructed to read the online consent form, complete the questionnaires, and later debriefed upon completion. Participation in the study was voluntary and participants received a credit towards their psychology course. Previous findings showed first-generation Asian Americans have views less associated with independent Western worldviews and lesser U.S. assimilation compared to second-generation Asian groups (Benet-Martínez & Karakitapoglu-Aygün, 2003). Given the nature of the research question, participants who were born in Canada and identified as European White and participants who were born in China who identified as Asian were directly compared. The European White sample born in Canada consists of 489 participants (ages ranged from 17 to 36 years; M = 18.96, SD = 2.20; 69.9% females) and the Chinese sample born in China consists of 147 participants (ages ranged from 17 to 24 years; M = 19.62, SD = 1.73; 70.7% females). The study was approved by the university's local institutional review board.

State-Trait Cheerfulness Inventory-Trait Version
The standard version of the State Trait Cheerfulness Inventory-Trait Version Ruch et al., 1996) is comprised of 60 items providing scores on three factors relating to the theoretically-derived temperamental basis of sense of humor (i.e., cheerfulness, seriousness, bad mood). The constructs are measured on a four-point Likert-style scale ranging from 1 to 4 (1 = strongly disagree; 4 = strongly agree).

State-Trait Cheerfulness Inventory-State Version
The State Trait Cheerfulness Inventory-State Version (STCI-S30; Ruch et al., 1997) was designed to measure cheerful ness, seriousness, and bad mood as current states. The standard version is comprised of 30 items, with 10 items measuring each factor, and respondents utilized a four-point scale (1 = strongly disagree, 4 = strongly agree). Each factor has subcategories representative of the global latent states for cheerfulness (i.e., cheerful mood and hilarity), seriousness (i.e., earnest, pensiveness, soberness), and bad mood (i.e., sadness/melancholy, ill-humor). Ruch and colleagues (1997) published several versions of the STCI state version (e.g., "today, " "the past hour"), but the present study assessed current state (i.e., "right now").

Data Analysis
The 60 items of the STCI-T60 and the 30 items of the STCI-S30 were subjected to two separate single-group confirma tory factor analyses (CFA) with maximum likelihood estimation using item parcels to test the three-factor structure proposed by colleagues (1996, 1997). The parceling procedure was applied based on the theoretical model by colleagues (1996, 1997) to lower measurement error and manage any inherent non-normality from single item distributions (Gribbons & Hocevar, 1998;Little, Cunningham, Shahar, & Widaman, 2002). Other researchers have provided adequate justification for the use of these parcels (e.g., Carretero-Dios, Benítez, Delgado-Rico, Ruch, & López-Benítez, 2014;Hofmann et al., 2018;Ruch et al., 1996Ruch et al., , 1997. Unidimensionality has been verified based on parallel analysis prior to item parcelling (Ferrando & Lorenzo-Seva, 2017). Detailed descriptions and examples of items for each parcel are provided in the Appendix. Hu and Bentler (1999) suggested that model fit should be evaluated using the Root Mean Square Error of Approxima tion (RMSEA), Tucker-Lewis Index (TLI) and Comparative Fit Index (CFI). Byrne (2001Byrne ( , 2012 indicated a RMSEA value of approximately 0.10 and 0.06 would suggest moderate and excellent model fit, respectively. A CFI and TLI in the range of 0.90 and 0.95 would suggest moderate and excellent model fit, respectively. Multigroup confirmatory factor analysis (MG-CFA) was used to examine invariance allowing sequences of progres sively restrictive models (Byrne, 2012;Hong, Malik, & Lee, 2003;Meredith, 1993;Steenkamp & Baumgartner, 1998). Specifically, configural, metric, scalar, and uniqueness invariance were evaluated in a successive manner. Configural invariance involved the establishment of a baseline model that acquires the equivalent pattern of parameters (i.e., same number[s] of factor[s], same items or parcels per factor) across groups. Metric invariance (i.e., weak factorial invariance) is established when the factor pattern coefficients are constrained to equality across groups, suggesting observed differences amongst parcels reveal true differences across groups (Hong et al., 2003;Steenkamp & Baumgartner, 1998). Uniqueness invariance (i.e., strict factorial invariance) is established when error terms are constrained to equality across groups. Finally, since the STCI encompasses a multidimensional structure, factor variances and covariances invariance was also tested constraining to equality covariances of the structural part of the model.
In the sequential assessment of the models, these models are typically compared using a chi-square-based likelihood ratio test. The χ 2 statistic is greatly sensitive to loss of fit with incremental invariance restrictions in large samples and thus, the equality constraints were tested with ΔCFI value ≤ 0.01 (Byrne, 2012;Cheung & Rensvold, 2002) supplemented by a change ≤ 0.015 in RMSEA would indicate invariance (Byrne, 2012;Cheung & Rensvold, 2002). These analyses determined whether the more restrictive model demonstrated worse fit than the previously-examined, less restrictive model (Byrne, 2012;Milfont & Fischer, 2010). When poor fit emerged, partial invariance of the most restrictive model was tested through releasing some parameters according to the model of invariance being examined (i.e., factor loadings, intercept, structural covariances, residuals for evaluating metric, scalar and factor variances and covariances, and uniqueness invariance, respectively).
Through establishing scalar (i.e., strong) invariance, or at least partial scalar invariance, meaningful comparisons across groups can be conducted. These analyses reflect meaningful cultural differences between culturally different groups rather than measurement biases (Byrne, 2012). In other words, this level of invariance allows for latent mean comparison instead of comparing the respective raw means to evaluate meaningful group differences (Milfont & Fischer, 2010;Wu, Chen, & Tsai, 2009). Additionally, uniqueness (i.e. strict) invariance between the two models is desirable even if meaningful group differences are performed at a scalar level (Gregorich, 2006). For this study, once the strong and strict invariances were tested, the latent means of the STCI factors were compared. Since the mean of a latent variable cannot be directly estimated, the European Canadian group mean was fixed to zero to estimate the difference between the means (Byrne, 2001). All statistical analyses were conducted on SPSS version 25 and SPSS AMOS 5.0 (Arbuckle, 2003).

Descriptive Statistics and Reliability
Means, standard deviations, and bivariate correlations of the STCI-T60 and STCI-S30 for European Canadians and Chinese Canadians are presented (Table 1). To examine normality of item parcels, univariate distributions were exam ined. For the trait version, skewness indices ranged from −0.98 to 0.42 and -0.45 to 0.37 for European and Chinese participants, respectively. Kurtosis indices for the trait version ranged from −0.56 to 1.02 and -0.69 to 1.06 for European and Chinese participants, respectively. Similarly, skewness indices for the state version ranged from −0.16 to 0.57 and -0.30 to 0.43 for European and Chinese participants, respectively. Kurtosis indices for the state version ranged from −0.65 to 0.04 and −0.35 to 0.31 for European and Chinese participants, respectively. These values suggest no significant departures from normality (Marcoulides & Hershberger, 1997;Muthén & Kaplan, 1985).

One-Group CFA for Model Testing
First, a preliminary single-group CFA was conducted to examine the factorial structure of the STCI-T60 for European White and Chinese Canadian participants separately. The CFA of the three-factor model for the European White participants born in Canada showed an adequate fit, χ 2 (74) = 366.62, p < .001, χ 2 /df = 4.95, CFI = .92, TLI = 0.90, RMSEA = .09. Factor loadings ranged from .74 to .86 for cheerfulness, .54 to .69 for seriousness, and .75 to .90 for bad mood. In terms of the structural model, seriousness was not associated with either cheerfulness or bad mood while cheerfulness and bad mood were strongly negatively associated (r = -.78, p < .001). Likewise, the CFA of the three-factor trait model for the Chinese participants born in China showed an adequate fit: χ 2 (74) = 150.24, p < .001, χ 2 /df = 2.03, CFI = .92, TLI = 0.90, RMSEA = .08. Factor loadings ranged from .69 to .86 for cheerfulness, .42 to .70 for seriousness, and .73 to .85 for bad mood. In terms of the structural model, seriousness was positively associated with cheerfulness (r = .23, p < .05) and bad mood (r = .32, p < .05), and cheerfulness and bad mood were strongly negatively associated (r = -.57, p < .001).

Multi-Group CFA for Measurement Invariance Testing
Starting from the single group CFA results, the baseline model for invariance testing was defined and configural invariance was tested. The configural model with the same set of factors fixed and free parameters across groups was well-fitting (see Model 0 in Table 2) in its representation of the multigroup data (Horn, McArdle, & Mason, 1983;Meredith, 1993). Metric invariance was established through constraining the equality of factor loadings. Compared with the config ural model, invariance restrictions placed on factor loadings did not lead to a significant decrement in model fit (ΔCFI < 0.01; see Model 1 in Table 2). These results indicate adding invariance restrictions on factor loadings did not lead to a significant decrement in model fit compared to the configural model. Note. df = degrees of freedom; CFI = comparative fit index; RMSEA = root mean square error of approximation; 90% CI = 90% confidence interval around RMSEA; ∆χ 2 = difference in χ 2 ; ∆df = difference in degrees of freedom; ∆CFI = difference between CFIs; ∆RMSEA = difference in root mean square error of approximation; τCH5 = intercept of parcel CH5; τSE5 = intercept of parcel SE5; CH = Cheerfulness; SE = Seriousness.
Compared to the metric invariance model, scalar invariance (see Model (2) was not established as a significant change in CFI was detected (ΔCFI = .02; see Model 2 -Model 1 in Table 2), suggesting at the same level of the latent factor, the threshold of the noninvariant parcels was different across groups. These results suggest that the endorsed levels of the underlying facets differed significantly across European White and Chinese participants. Two partial scalar models were specified with one freeing the τCH5 (i.e., CH5 representing generally cheerful interaction style) intercept of the parcel across groups (Model 2a), and the other freeing both τCH5 and τSE5 (i.e., SE5 representing preference for a sober, object-oriented communication style; Model 2b). Freeing the two specific thresholds in Model 2b led to an acceptable change in CFI for the partial scalar model when compared with the weak invariance model (ΔCFI = .01; see Model 2b -Model 1). Thus, Model 2b was selected as the final model for this step. Before establishing strict invariance, factor variances and covariances were constrained to be equal across group (Model 3) and fit indices with ∆CFI values compared to Model 2b indicated invariance. Similarly, when error terms were constrained to equality across groups (Model 4), fit indices and ΔCFI values indicated invariance.

Latent Mean Differences
In order to examine latent factor means between European White and Chinese Canadian students, the observed variable intercepts were constrained equal across the Canadian and Chinese groups for Model 2b (i.e., τCH5 and τSE5 free for partial scalar invariance; Byrne, 2012). In comparing latent means, constraints for CH5 and SE5 were deleted, but the cheerfulness and seriousness factors have four remaining invariant intercepts per factor (i.e., parcels). Estimates derived from this solution may be estimated accurately as the structural means model fit the data adequately with the constraints on the intercept, χ 2 (171) = 586.70, CFI = .91, RMSEA = .06. European Canadian participants reported significantly higher cheerfulness, z = 3.30, p < .001, d = 0.84, and lower bad mood z = 3.25, p < .01, d = 0.80 compared to the Chinese Canadian groups. No significant difference between the groups was observed for seriousness, z = 1.12, p = .27.

One-Group CFA for Model Testing
Similar to the trait version, a preliminary single-group CFA was conducted to examine the factorial structure of the STCI-S30 instrument for European White and Chinese Canadians separately. The CFA of the three-factor model for European White participants born in Canada showed a good fit, χ 2 (11) = 24.35, p < .05, χ 2 /df = 2.21, CFI = .99, TLI = 0.99, RMSEA = .05. Factor loadings ranged from .90 to .95 for state cheerfulness, .52 to .79 for state seriousness, and .88 to .96 for state bad mood. In terms of the structural model, states cheerfulness and seriousness were positively associated (r = .18, p < .01) and states cheerfulness and bad mood were strongly negatively associated (r = -.76, p < .001).
The CFA of the three-factor model for Chinese participants born in China showed a good fit, χ 2 (12) = 25.52, p < .05, χ 2 /df = 2.126, CFI = .97, TLI = 0.94, RMSEA = .09. Factor loadings ranged from .74 to .97 for state cheerfulness, .56 to .74 for state seriousness, and .87 to .93 for state bad mood. In terms of the structural model, state seriousness was not associated with either states cheerfulness or bad mood while states cheerfulness and bad mood were strongly negatively associated (r = -.66, p < .001).
Configural invariance was tested to determine whether the number of factors for the state version were invariant across Canadian and Chinese groups. The configural model was well-fitting (see Model 0 in Table 3) in its representation of the multigroup data. Furthermore, invariance restrictions placed on measurement weights did not lead to a significant decrement in model fit compared with the configural model (ΔCFI = .009; see Model 1 -Model 0 in Table 3). These results suggest metric invariance can be established as the associations between the state factors and individual parcels were not significantly different across these two groups. Note. df = degrees of freedom; CFI = comparative fit index; RMSEA = root mean square error of approximation; 90% CI = 90% confidence interval around RMSEA;∆χ 2 = difference in χ 2 ; ∆df = difference in degrees of freedom; ∆CFI = Difference between CFIs; ∆RMSEA = difference in root mean square error of approximation; B1 = intercept of parcel in the factor Bad Mood, representing a state of sad mood.
Compared to the metric invariance model, scalar invariance (Model (2) was not established as a significant change in CFI was detected (ΔCFI = .012; Model 2 -Model 1), suggesting at the same level of the latent factor, the threshold of the noninvariant parcels was different across groups. These results suggest that the endorsed levels of the underlying facets differed significantly across European White and Chinese participants. Thus, a modification of freeing one of the parcels (i.e., B1 from the factor state bad mood representing state sadness) was conducted. Freeing one specific threshold in Model 2a led to an acceptable change in CFI for the partial scalar model when compared with the metric invariance model. Thus, Model 2a was selected as the final model for this step.
Before establishing strict invariance, factor variances and covariances were constrained to be equal across group (Model 3) and the ΔCFI and ΔRMSEA values indicated invariance in comparison with Model 2a. When error terms were constrained to equality across groups (Model 4), fit indices and ΔCFI values indicated invariance when compared with Model 3.

Latent Mean Differences
In order to examine latent factor means between European White and Chinese Canadian students, the observed variable intercepts were constrained equal across the Canadian and Chinese groups for Model 2a (i.e., τ of parcel representing state sadness in the factor state bad mood free for partial scalar invariance; Byrne, 2012). The structural means model fit the data adequately with the constraints on the intercept, χ 2 (35) = 96.46, CFI = .97, RMSEA = .05. Given this finding, estimates derived from this solution may be estimated accurately. European White Canadian participants reported significantly lower state bad mood compared to the Chinese Canadian groups, z = 3.59, p < .001, d = 1.15. No significant difference between the groups was observed for state seriousness, z = 0.45, p = .66, or state cheerfulness, z = -0.65, p = 52.

Discussion
The present study contributed to growing literature in cross-cultural studies in humor through providing empirical evidence supporting partial strong measurement invariance of the STCI trait and state forms across first generation Chinese and European White Canadian participants. The results demonstrated that the measurement structures of cheerfulness, seriousness, and bad mood were largely equivalent across European White participants born in Canada and first generation Chinese Canadian participants born in China. Metric invariance was found for both the state and trait versions of the STCI. Upon freeing two intercepts, partial scalar invariance was found for the trait version of the STCI, which indicates cross-cultural similarity for the interpretation of the three dimensions. For the state version, upon freeing one intercept, partial scalar invariance was found. The proportion of invariant to non-invariant threshold parameters should allow fair comparisons between groups (Byrne, Shavelson, & Muthén, 1989). These findings provide evidence supporting the generalizability of the three-factor model of the temperamental basis of humor in Chinese participants (Chen et al., 2017;Lau et al., 2020).
In a previous study comparing the Chinese and English version of the STCI, noninvariant latent mean differences could not be compared given that only partial metric invariance was found (Lau et al., 2020). In the present study, the corresponding noninvariant latent factor means were examined. European White Canadian participants reported higher trait cheerfulness and lower trait bad mood compared to first generation Chinese Canadians. These results were consistent with previous findings showing Americans were more extraverted than Asians (McCrae & Terracciano, 2005). Indeed, trait cheerfulness is a narrow-level personality trait under the broader-level trait extraversion, but cheerfulness as an independent variable generally acts as a better predictor for specific humor-induced positive affect (Ruch & Hofmann, 2012). Moreover, these results align with findings that individualist cultures tend to promote positivity whereas dialectical cultures value balance of emotions (Tsai, Knutson, & Fung, 2006). As well, previous findings showed European Americans had better recall of positive affect but not negative affect, whereas Asian Americans equally recalled positive and negative affect (Wirtz, Chiu, Diener, & Oishi, 2009). Notably, Asian Canadians in this sample scored much higher in state bad mood than European White participants, but did not differ in state cheerfulness and state seriousness. Perhaps individuals of East Asian descent tend to endorse more contradictory elements in opposing emotions compared to European White North Americans who have not been exposed to dialecticism (Goetz, Spencer-Rodgers, & Peng, 2008;Spencer-Rodgers, Peng, & Wang, 2010).
The present study is not without its limitations. The sample comprised of well-educated young adults attending university and it is unclear whether these findings would generalize across different populations (i.e., difference in age, education). Furthermore, only a small sample of the Canadians recruited were second generation Chinese Canadians and of other Asian backgrounds (e.g., Korean, Japanese). These factors precluded the present study to further investigate similarities and differences between other English-speaking Asian Canadians. Moreover, the nature of humor is a multidimensional phenomenon that encompasses a function (e.g., pro-social or mean-spirited) and fulfills complex needs for the individual (e.g., engage with others, mock others). Future studies should test whether the STCI in Chinese participants predicts similar behavioral outcomes that were found in previous studies (e.g., Duchenne displays, positive benign styles of humor, frequency and intensity of laughter).
In summary, the present study extends earlier findings for a well-fitting three-factor model in the temperamental basis of humor for first generation Chinese Canadian participants. Findings from the present study provide a founda tional basis for the utility of the STCI in studying the temperamental basis of humor for first generation Chinese North Americans. This study addresses concerns of extending Western models to individuals born to non-Western cultures (Gerstein & AEgisdóttir, 2012). Future studies can utilize this measure to investigate associations between the temperamental basis of humor and acculturation in North America.  Note. N i = number of items.