Approach & Conclusion
Originally, I have obtained a model with 6 Factors; however, after some discussions and comments, I have decided to merge some of the factors and their manifest variables into a single factor because correlations between factors were large (> 0.9). The result of this is the first-order model below with 4 factors.
I have also attempted to fit the hierarchical model, the bi-factor model, and finally the single-factor model.
The best-fit seems to be reached with the hierarchical model (second-order model). The bi-factor model suggests that the solution with the single factor is favoured because domain factors have bad loadings after accounting for the single factor. Fit indices are in favour of the hierarchical model; however, factors correlate in nearly all instances > 0.5 with each other and the global factor which tells me that I should consider the single-factor model.
I was deciding between the hierarchical model and the single-factor model. However, the single-factor seems like a more parsimonious and straightforward solution, hence, I am decided to use this model at the moment. You can see elementary comparison below.
Single factor model vs. Higher order model
| fit_single_factor |
299 |
10773 |
10954 |
1370 |
NA |
NA |
NA |
| fit_4_factors_hierarchical |
346 |
11565 |
11773 |
1147 |
-223 |
47 |
1 |
Please proceed below to see details of all models, fit indices, loadings, and plots.
First order model (Consists of 4 factors)
First order; Factor loadings
| IMPR1 |
0.69 |
0.00 |
0.00 |
0.00 |
| IMPR2 |
0.87 |
0.00 |
0.00 |
0.00 |
| IMPR3 |
0.89 |
0.00 |
0.00 |
0.00 |
| IMPR4 |
0.34 |
0.00 |
0.00 |
0.00 |
| IMPR5 |
0.61 |
0.00 |
0.00 |
0.00 |
| GEN1 |
0.00 |
0.84 |
0.00 |
0.00 |
| GEN2neg |
0.00 |
0.12 |
0.00 |
0.00 |
| GEN3 |
0.00 |
0.16 |
0.00 |
0.00 |
| GEN4neg |
0.00 |
0.24 |
0.00 |
0.00 |
| GEN5 |
0.00 |
0.86 |
0.00 |
0.00 |
| SEL1 |
0.00 |
0.00 |
0.89 |
0.00 |
| SEL2neg |
0.00 |
0.00 |
0.82 |
0.00 |
| SEL3neg |
0.00 |
0.00 |
0.82 |
0.00 |
| SEL4 |
0.00 |
0.00 |
0.90 |
0.00 |
| SEL5 |
0.00 |
0.00 |
0.81 |
0.00 |
| TRU1neg |
0.00 |
0.00 |
0.00 |
0.81 |
| TRU2 |
0.00 |
0.00 |
0.00 |
0.68 |
| TRU3neg |
0.00 |
0.00 |
0.00 |
0.55 |
| TRU4neg |
0.00 |
0.00 |
0.00 |
0.40 |
| TRU5 |
0.00 |
0.00 |
0.00 |
0.61 |
| CRE1neg |
0.00 |
0.00 |
0.00 |
0.77 |
| CRE2 |
0.00 |
0.00 |
0.00 |
0.77 |
| CRE3 |
0.00 |
0.00 |
0.00 |
0.78 |
| CRE4 |
0.00 |
0.00 |
0.00 |
0.82 |
| CRE5neg |
0.00 |
0.00 |
0.00 |
0.69 |
| COMP1 |
0.00 |
0.00 |
0.00 |
0.70 |
| COMP2 |
0.00 |
0.00 |
0.00 |
0.79 |
| COMP3 |
0.00 |
0.00 |
0.00 |
0.78 |
| COMP4 |
0.00 |
0.00 |
0.00 |
0.66 |
| COMP5 |
0.00 |
0.00 |
0.00 |
0.67 |
First order; Correlation matrix of the latent variables
| Impression |
1.00 |
0.43 |
0.71 |
0.75 |
| Adherence |
0.43 |
1.00 |
0.63 |
0.65 |
| Selectability |
0.71 |
0.63 |
1.00 |
0.92 |
| Trust_Credibility_Compassion |
0.75 |
0.65 |
0.92 |
1.00 |
First order; Fit measures
| npar |
66.000 |
| fmin |
2.774 |
| chisq |
1314.986 |
| df |
399.000 |
| pvalue |
0.000 |
| baseline.chisq |
5368.605 |
| baseline.df |
435.000 |
| baseline.pvalue |
0.000 |
| cfi |
0.814 |
| tli |
0.798 |
| nnfi |
0.798 |
| rfi |
0.733 |
| nfi |
0.755 |
| pnfi |
0.693 |
| ifi |
0.816 |
| rni |
0.814 |
| logl |
-6218.072 |
| unrestricted.logl |
-5560.579 |
| aic |
12568.143 |
| bic |
12797.035 |
| ntotal |
237.000 |
| bic2 |
12587.838 |
| rmsea |
0.098 |
| rmsea.ci.lower |
0.093 |
| rmsea.ci.upper |
0.104 |
| rmsea.pvalue |
0.000 |
| rmr |
0.045 |
| rmr_nomean |
0.045 |
| srmr |
0.073 |
| srmr_bentler |
0.073 |
| srmr_bentler_nomean |
0.073 |
| crmr |
0.076 |
| crmr_nomean |
0.076 |
| srmr_mplus |
0.073 |
| srmr_mplus_nomean |
0.073 |
| cn_05 |
81.486 |
| cn_01 |
85.283 |
| gfi |
0.712 |
| agfi |
0.665 |
| pgfi |
0.611 |
| mfi |
0.145 |
| ecvi |
6.105 |
Higher order model
Higher order model; Factor loadings
| IMPR1 |
0.69 |
0.00 |
0.00 |
0.00 |
0 |
| IMPR2 |
0.87 |
0.00 |
0.00 |
0.00 |
0 |
| IMPR3 |
0.89 |
0.00 |
0.00 |
0.00 |
0 |
| IMPR4 |
0.34 |
0.00 |
0.00 |
0.00 |
0 |
| IMPR5 |
0.61 |
0.00 |
0.00 |
0.00 |
0 |
| GEN1 |
0.00 |
0.84 |
0.00 |
0.00 |
0 |
| GEN4neg |
0.00 |
0.23 |
0.00 |
0.00 |
0 |
| GEN5 |
0.00 |
0.87 |
0.00 |
0.00 |
0 |
| SEL1 |
0.00 |
0.00 |
0.89 |
0.00 |
0 |
| SEL2neg |
0.00 |
0.00 |
0.82 |
0.00 |
0 |
| SEL3neg |
0.00 |
0.00 |
0.82 |
0.00 |
0 |
| SEL4 |
0.00 |
0.00 |
0.90 |
0.00 |
0 |
| SEL5 |
0.00 |
0.00 |
0.81 |
0.00 |
0 |
| TRU1neg |
0.00 |
0.00 |
0.00 |
0.81 |
0 |
| TRU2 |
0.00 |
0.00 |
0.00 |
0.68 |
0 |
| TRU3neg |
0.00 |
0.00 |
0.00 |
0.55 |
0 |
| TRU4neg |
0.00 |
0.00 |
0.00 |
0.40 |
0 |
| TRU5 |
0.00 |
0.00 |
0.00 |
0.61 |
0 |
| CRE1neg |
0.00 |
0.00 |
0.00 |
0.77 |
0 |
| CRE2 |
0.00 |
0.00 |
0.00 |
0.77 |
0 |
| CRE3 |
0.00 |
0.00 |
0.00 |
0.78 |
0 |
| CRE4 |
0.00 |
0.00 |
0.00 |
0.82 |
0 |
| CRE5neg |
0.00 |
0.00 |
0.00 |
0.69 |
0 |
| COMP1 |
0.00 |
0.00 |
0.00 |
0.70 |
0 |
| COMP2 |
0.00 |
0.00 |
0.00 |
0.79 |
0 |
| COMP3 |
0.00 |
0.00 |
0.00 |
0.78 |
0 |
| COMP4 |
0.00 |
0.00 |
0.00 |
0.65 |
0 |
| COMP5 |
0.00 |
0.00 |
0.00 |
0.67 |
0 |
Higher order model; Correlation matrix of the latent variables
| Impression |
1.00 |
0.50 |
0.71 |
0.74 |
0.76 |
| Adherence |
0.50 |
1.00 |
0.62 |
0.64 |
0.66 |
| Selectability |
0.71 |
0.62 |
1.00 |
0.92 |
0.94 |
| Trust_Credibility_Compassion |
0.74 |
0.64 |
0.92 |
1.00 |
0.98 |
| Global |
0.76 |
0.66 |
0.94 |
0.98 |
1.00 |
Higher order model; Fit measures
| npar |
60.00000000000000 |
| fmin |
2.41914009475886 |
| chisq |
1146.67240491569919 |
| df |
346.00000000000000 |
| pvalue |
0.00000000000000 |
| baseline.chisq |
5188.66030622200378 |
| baseline.df |
378.00000000000000 |
| baseline.pvalue |
0.00000000000000 |
| cfi |
0.83356288867869 |
| tli |
0.81816986104203 |
| nnfi |
0.81816986104203 |
| rfi |
0.75856522531303 |
| nfi |
0.77900414803785 |
| pnfi |
0.71305670693412 |
| ifi |
0.83466269482355 |
| rni |
0.83356288867869 |
| logl |
-5722.57881304458078 |
| unrestricted.logl |
-5149.24261058673073 |
| aic |
11565.15762608916157 |
| bic |
11773.24123455727022 |
| ntotal |
237.00000000000000 |
| bic2 |
11583.06220938417573 |
| rmsea |
0.09881325555375 |
| rmsea.ci.lower |
0.09251148663735 |
| rmsea.ci.upper |
0.10517878615873 |
| rmsea.pvalue |
0.00000000000008 |
| rmr |
0.04177584556157 |
| rmr_nomean |
0.04177584556157 |
| srmr |
0.06791218523506 |
| srmr_bentler |
0.06791218523506 |
| srmr_bentler_nomean |
0.06791218523506 |
| crmr |
0.07038250207747 |
| crmr_nomean |
0.07038250207747 |
| srmr_mplus |
0.06791216644056 |
| srmr_mplus_nomean |
0.06791216644056 |
| cn_05 |
81.68490806311753 |
| cn_01 |
85.76582480575274 |
| gfi |
0.71937725929067 |
| agfi |
0.67071435627749 |
| pgfi |
0.61306534905067 |
| mfi |
0.18467046937129 |
| ecvi |
5.34460930344177 |
Bi-factor model
Bi-factor model; Factor loadings
| IMPR1 |
0.42 |
0.00 |
0.00 |
0.00 |
0.54 |
| IMPR2 |
0.45 |
0.00 |
0.00 |
0.00 |
0.73 |
| IMPR3 |
0.71 |
0.00 |
0.00 |
0.00 |
0.61 |
| IMPR4 |
0.37 |
0.00 |
0.00 |
0.00 |
0.15 |
| IMPR5 |
0.47 |
0.00 |
0.00 |
0.00 |
0.41 |
| GEN1 |
0.00 |
0.82 |
0.00 |
0.00 |
0.53 |
| GEN2neg |
0.00 |
-0.04 |
0.00 |
0.00 |
0.17 |
| GEN3 |
0.00 |
0.16 |
0.00 |
0.00 |
0.04 |
| GEN4neg |
0.00 |
0.31 |
0.00 |
0.00 |
0.07 |
| GEN5 |
0.00 |
0.52 |
0.00 |
0.00 |
0.58 |
| SEL1 |
0.00 |
0.00 |
0.31 |
0.02 |
0.81 |
| SEL2neg |
0.00 |
0.00 |
0.54 |
0.00 |
0.72 |
| SEL3neg |
0.00 |
0.00 |
0.46 |
0.05 |
0.73 |
| SEL4 |
0.00 |
0.00 |
0.27 |
0.07 |
0.84 |
| SEL5 |
0.00 |
0.00 |
0.14 |
0.11 |
0.78 |
| TRU1neg |
0.00 |
0.00 |
0.00 |
-0.15 |
0.83 |
| TRU2 |
0.00 |
0.00 |
0.00 |
0.28 |
0.65 |
| TRU3neg |
0.00 |
0.00 |
0.00 |
0.26 |
0.52 |
| TRU4neg |
0.00 |
0.00 |
0.00 |
0.35 |
0.37 |
| TRU5 |
0.00 |
0.00 |
0.00 |
0.14 |
0.60 |
| CRE1neg |
0.00 |
0.00 |
0.00 |
-0.13 |
0.79 |
| CRE2 |
0.00 |
0.00 |
0.00 |
0.02 |
0.78 |
| CRE3 |
0.00 |
0.00 |
0.00 |
-0.12 |
0.80 |
| CRE4 |
0.00 |
0.00 |
0.00 |
-0.25 |
0.86 |
| CRE5neg |
0.00 |
0.00 |
0.00 |
-0.20 |
0.71 |
| COMP1 |
0.00 |
0.00 |
0.00 |
0.34 |
0.67 |
| COMP2 |
0.00 |
0.00 |
0.00 |
0.30 |
0.77 |
| COMP3 |
0.00 |
0.00 |
0.00 |
0.43 |
0.75 |
| COMP4 |
0.00 |
0.00 |
0.00 |
0.35 |
0.62 |
| COMP5 |
0.00 |
0.00 |
0.00 |
0.36 |
0.64 |
Bi-factor model; Correlation matrix of the latent variables
| Impression |
1 |
0 |
0 |
0 |
0 |
| Adherence |
0 |
1 |
0 |
0 |
0 |
| Selectability |
0 |
0 |
1 |
0 |
0 |
| Trust_Credibility_Compassion |
0 |
0 |
0 |
1 |
0 |
| Single |
0 |
0 |
0 |
0 |
1 |
Bi-factor model; Fit measures
| npar |
95.00000000000000 |
| fmin |
2.09504545612137 |
| chisq |
993.05154620152894 |
| df |
370.00000000000000 |
| pvalue |
0.00000000000000 |
| baseline.chisq |
5368.60508593987561 |
| baseline.df |
435.00000000000000 |
| baseline.pvalue |
0.00000000000000 |
| cfi |
0.87371272419490 |
| tli |
0.85152712168860 |
| nnfi |
0.85152712168860 |
| rfi |
0.78253074516155 |
| nfi |
0.81502615105695 |
| pnfi |
0.69324063423235 |
| ifi |
0.87535491692391 |
| rni |
0.87371272419490 |
| logl |
-6057.10452586811334 |
| unrestricted.logl |
-5560.57875276734831 |
| aic |
12304.20905173622668 |
| bic |
12633.67476514406371 |
| ntotal |
237.00000000000000 |
| bic2 |
12332.55797528666517 |
| rmsea |
0.08429211558852 |
| rmsea.ci.lower |
0.07798843318219 |
| rmsea.ci.upper |
0.09063995091353 |
| rmsea.pvalue |
0.00000000000015 |
| rmr |
0.03555550372543 |
| rmr_nomean |
0.03555550372543 |
| srmr |
0.05781384948720 |
| srmr_bentler |
0.05781384948720 |
| srmr_bentler_nomean |
0.05781384948720 |
| crmr |
0.05977419278508 |
| crmr_nomean |
0.05977419278508 |
| srmr_mplus |
0.05781384742537 |
| srmr_mplus_nomean |
0.05781384742537 |
| cn_05 |
100.24670364867860 |
| cn_01 |
105.10472624420488 |
| gfi |
0.77857884048612 |
| agfi |
0.72172746169201 |
| pgfi |
0.61951434619325 |
| mfi |
0.26862075178232 |
| ecvi |
4.99177867595582 |
Single factor model
Single factor model; Factor loadings
| IMPR1 |
0.57 |
| IMPR2 |
0.74 |
| IMPR3 |
0.65 |
| IMPR5 |
0.44 |
| GEN1 |
0.54 |
| GEN5 |
0.59 |
| TRU1neg |
0.79 |
| TRU2 |
0.66 |
| TRU3neg |
0.54 |
| TRU4neg |
0.39 |
| TRU5 |
0.60 |
| CRE1neg |
0.76 |
| CRE2 |
0.77 |
| CRE3 |
0.77 |
| CRE4 |
0.82 |
| CRE5neg |
0.70 |
| COMP1 |
0.68 |
| COMP2 |
0.76 |
| COMP3 |
0.76 |
| COMP4 |
0.66 |
| COMP5 |
0.67 |
| SEL1 |
0.85 |
| SEL2neg |
0.77 |
| SEL3neg |
0.78 |
| SEL4 |
0.87 |
| SEL5 |
0.80 |
Single factor model; Correlation matrix of the latent variables
Single factor model; Fit measures
| npar |
52.000 |
| fmin |
2.890 |
| chisq |
1369.876 |
| df |
299.000 |
| pvalue |
0.000 |
| baseline.chisq |
4999.198 |
| baseline.df |
325.000 |
| baseline.pvalue |
0.000 |
| cfi |
0.771 |
| tli |
0.751 |
| nnfi |
0.751 |
| rfi |
0.702 |
| nfi |
0.726 |
| pnfi |
0.668 |
| ifi |
0.772 |
| rni |
0.771 |
| logl |
-5334.692 |
| unrestricted.logl |
-4649.754 |
| aic |
10773.383 |
| bic |
10953.722 |
| ntotal |
237.000 |
| bic2 |
10788.901 |
| rmsea |
0.123 |
| rmsea.ci.lower |
0.116 |
| rmsea.ci.upper |
0.130 |
| rmsea.pvalue |
0.000 |
| rmr |
0.043 |
| rmr_nomean |
0.043 |
| srmr |
0.072 |
| srmr_bentler |
0.072 |
| srmr_bentler_nomean |
0.072 |
| crmr |
0.075 |
| crmr_nomean |
0.075 |
| srmr_mplus |
0.072 |
| srmr_mplus_nomean |
0.072 |
| cn_05 |
59.880 |
| cn_01 |
63.077 |
| gfi |
0.661 |
| agfi |
0.602 |
| pgfi |
0.563 |
| mfi |
0.104 |
| ecvi |
6.219 |
