As mentioned earlier, the measurement model must be identified prior to model testing and only one item is linked to a factor. Figure 1 shows the measurement model.
The constructs used in the CFA model are the same constructs presented in the previous section (Theory questions): attitude, anticipated emotion, subjective norms, group norms, perceived behavioral control, past game and service satisfaction, fan engagement, team identity, fan community identity, desires, and behavioral intentions. Each of the constructs will be measured with scales that have been used and validated in the previous studies.
For CFA assessing the model fit is important. When model fit is not satisfactory, this means that the measurement model does not represent the collected data well, so modification is necessary until the model fit improves or another set of data should be collected. Model Fit indices are controversial for a number of reasons. First, only the chi-square test is a true statistical test of model fit; however, as sample size increases above 200 (see Hu & Bentler, 1999), the likelihood for type II error (false rejection) increases. Given that SEM is an asymptotic (large sample) technique, this is problematic. Therefore, other model fit indices have been designed to address these limitations, focusing on different dimensions of model fit. Tanaka (1993) identifies six (6) dimensions of model fit: (1) Absolute vs. Relative (incremental); (2) Simple vs. Complex; (3) Normed vs. Non-normed; (4) Population vs. Sample; (5) Estimation Method Independent vs. Estimation Method Dependent; and (6) Sample-size Dependent vs. Sample-size Independent. Hu and Bentler (1999) suggested four dimensions of fit indices and Kline (2010) suggested three dimensions (i.e., absolute, relative, and predictive). I will examine following fit indices. Chi-square It should always be reported. It is an exact test of whether the model fits the data. Actually, it is a “badness of fit” index (i.e., larger numbers are better) so researchers want to receive a non-significant finding. A large problem with chi-square is that it is sensitive to sample size. Normed Chi-square It is the chi-square divided by the degrees of freedom. As an attempt to help mitigate the issues of the sample size issue on chi-square, researchers have begun to subscribe to the idea that if they use the normed chi-square, their problems will be fixed. But this is a fallacy (Kline, 2010). The degree of freedom does not have anything to do with sample size. Dividing by it does not make sense. Another criticism is that there are no good cutoff values established (Kline, 2010). Bollen (1989) recommends a maximum ratio cut-off of 2.0 or 3.0; however, he mentions that sometimes a cut-off of 5.0 has been found to be adequate. SRMR (Standardized Root Mean Square Residual) This is calculated as the differences between the observed and reproduced correlation matrices. It is estimation method free. Lower results are better—zero indicates perfect fit. Hu and Bentler (1998) recommend a cutoff of 0.05 for good fit and 0.08 for acceptable fit. A problem with this is that at 0.08, there can be a number of correlation residuals that …show more content…
Construct validity is examined through both convergent validity and discriminant validity. Convergent validity will be established by examining average variance extracted (AVE) values (>.5; Hair et al., 2009). Composite reliability (CR) will be calculated to assess the construct level reliability. Discriminant validity will examine the degree of discriminant level among the factors to make sure that each factor is not measuring the same factor. This is accomplished using the square of the coefficient smaller than AVE, which represents its correlation with other constructs (Fornell & Larcker, 1981). Furthermore, the reliability of the factors and the observed variables will be examined by Cronbach’s alpha (>.7; Nunnally, …show more content…
Hence, measurement of the observed variables are perfect, meaning normality of residuals, equality of the variance, independency of the error terms, and linearity are met (Bollen & Jackman, 1990). So the constructs or variables that are measured using the multiple regression method should be relatively clear. For example, Haumann et al. (2014), in their study, used 20 control variables to get more accurate effects of the variables in the model by controlling the excluded (from the model) variables’ influence on loyalty and
The constructs used in the CFA model are the same constructs presented in the previous section (Theory questions): attitude, anticipated emotion, subjective norms, group norms, perceived behavioral control, past game and service satisfaction, fan engagement, team identity, fan community identity, desires, and behavioral intentions. Each of the constructs will be measured with scales that have been used and validated in the previous studies.
For CFA assessing the model fit is important. When model fit is not satisfactory, this means that the measurement model does not represent the collected data well, so modification is necessary until the model fit improves or another set of data should be collected. Model Fit indices are controversial for a number of reasons. First, only the chi-square test is a true statistical test of model fit; however, as sample size increases above 200 (see Hu & Bentler, 1999), the likelihood for type II error (false rejection) increases. Given that SEM is an asymptotic (large sample) technique, this is problematic. Therefore, other model fit indices have been designed to address these limitations, focusing on different dimensions of model fit. Tanaka (1993) identifies six (6) dimensions of model fit: (1) Absolute vs. Relative (incremental); (2) Simple vs. Complex; (3) Normed vs. Non-normed; (4) Population vs. Sample; (5) Estimation Method Independent vs. Estimation Method Dependent; and (6) Sample-size Dependent vs. Sample-size Independent. Hu and Bentler (1999) suggested four dimensions of fit indices and Kline (2010) suggested three dimensions (i.e., absolute, relative, and predictive). I will examine following fit indices. Chi-square It should always be reported. It is an exact test of whether the model fits the data. Actually, it is a “badness of fit” index (i.e., larger numbers are better) so researchers want to receive a non-significant finding. A large problem with chi-square is that it is sensitive to sample size. Normed Chi-square It is the chi-square divided by the degrees of freedom. As an attempt to help mitigate the issues of the sample size issue on chi-square, researchers have begun to subscribe to the idea that if they use the normed chi-square, their problems will be fixed. But this is a fallacy (Kline, 2010). The degree of freedom does not have anything to do with sample size. Dividing by it does not make sense. Another criticism is that there are no good cutoff values established (Kline, 2010). Bollen (1989) recommends a maximum ratio cut-off of 2.0 or 3.0; however, he mentions that sometimes a cut-off of 5.0 has been found to be adequate. SRMR (Standardized Root Mean Square Residual) This is calculated as the differences between the observed and reproduced correlation matrices. It is estimation method free. Lower results are better—zero indicates perfect fit. Hu and Bentler (1998) recommend a cutoff of 0.05 for good fit and 0.08 for acceptable fit. A problem with this is that at 0.08, there can be a number of correlation residuals that …show more content…
Construct validity is examined through both convergent validity and discriminant validity. Convergent validity will be established by examining average variance extracted (AVE) values (>.5; Hair et al., 2009). Composite reliability (CR) will be calculated to assess the construct level reliability. Discriminant validity will examine the degree of discriminant level among the factors to make sure that each factor is not measuring the same factor. This is accomplished using the square of the coefficient smaller than AVE, which represents its correlation with other constructs (Fornell & Larcker, 1981). Furthermore, the reliability of the factors and the observed variables will be examined by Cronbach’s alpha (>.7; Nunnally, …show more content…
Hence, measurement of the observed variables are perfect, meaning normality of residuals, equality of the variance, independency of the error terms, and linearity are met (Bollen & Jackman, 1990). So the constructs or variables that are measured using the multiple regression method should be relatively clear. For example, Haumann et al. (2014), in their study, used 20 control variables to get more accurate effects of the variables in the model by controlling the excluded (from the model) variables’ influence on loyalty and