Original link: http://tecdat.cn/?p=10165
In practice, the load factor is low (or poor measurement quality) fitted exponential model is better than a higher load factor model. For example, if the two models have the same error level is specified, and the load factor of .9 RMSEA model may be higher than .2, whereas for the load factor of .4 RMSEA model may be less than .05. This article contains a chart, you can very clearly communicate these results.
AFIs It is fitting goodness index approximation, and the like, including RMSEA and SRMR absolute fit index, and other relatively fit index CFI.
Using global fitting alternative index
Written MAH fit index is a global fit index (hereinafter referred to as GFI), which detects all types of model specification is incorrect. But, as MAH pointed out that not all model specifications are not correct a problem. Consider the order effect, two items may have associated errors independent of its share factor, because it is only one item to another item follower (serial correlation). This error is not related to the presence of CFA will have a negative impact on any global fit index (default value) in. In addition, the global fit index does not tell you what the error model specification yes.
SSV presents a survey model specification incorrect method, the method involves using a modified index (MI), the expected parameters (EPC), theory and power analysis. EPC if the relationship is bound value can be estimated by the model of freedom, the relationship will change the zero bound. I believe that researchers familiar with MI, and often use them to fix the error model specifications, in order to obtain their reviewers can accept GFI. The relationship between MI and EPC are:
MI = (EPC / σ) = 2MI (EPC / σ) 2
SS
SSV recommends the following framework:
- (D) (d)
- For a load factor, the absolute value of> .4
- For correlation error, the absolute value> .1
- ncp = (d / p) 2ncp = (d / p) 2
- N c pncpχ 2χ2δδ
The following decision rule:
All these implementations in R.
library(lavaan)
For this reason, I assume that the data 9 questions, respondents answered in turn x1 to x9.
data("HolzingerSwineford1939")
# model syntax for HolzingerSwineford1939 dataset
(syntax <- paste(
paste("f1 =~", paste0("x", 1:3, collapse = " + ")),
paste("f2 =~", paste0("x", 4:6, collapse = " + ")),
paste("f3 =~", paste0("x", 7:9, collapse = " + ")),
sep = "\n"))
[1] "f1 =~ x1 + x2 + x3\nf2 =~ x4 + x5 + x6\nf3 =~ x7 + x8 + x9"
Running the model, standardized latent variables, and reporting standardization results:
lavaan (0.5-23.1097) converged normally after 22 iterations
Number of observations 301
Estimator ML
Minimum Function Test Statistic 85.306
Degrees of freedom 24
P-value (Chi-square) 0.000
Parameter Estimates:
Information Expected
Standard Errors Standard
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
f1 =~
x1 0.900 0.081 11.127 0.000 0.900 0.772
x2 0.498 0.077 6.429 0.000 0.498 0.424
x3 0.656 0.074 8.817 0.000 0.656 0.581
f2 =~
x4 0.990 0.057 17.474 0.000 0.990 0.852
x5 1.102 0.063 17.576 0.000 1.102 0.855
x6 0.917 0.054 17.082 0.000 0.917 0.838
f3 =~
x7 0.619 0.070 8.903 0.000 0.619 0.570
x8 0.731 0.066 11.090 0.000 0.731 0.723
x9 0.670 0.065 10.305 0.000 0.670 0.665
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
f1 ~~
f2 0.459 0.064 7.189 0.000 0.459 0.459
f3 0.471 0.073 6.461 0.000 0.471 0.471
f2 ~~
f3 0.283 0.069 4.117 0.000 0.283 0.283
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.x1 0.549 0.114 4.833 0.000 0.549 0.404
.x2 1.134 0.102 11.146 0.000 1.134 0.821
.x3 0.844 0.091 9.317 0.000 0.844 0.662
.x4 0.371 0.048 7.778 0.000 0.371 0.275
.x5 0.446 0.058 7.642 0.000 0.446 0.269
.x6 0.356 0.043 8.277 0.000 0.356 0.298
.x7 0.799 0.081 9.823 0.000 0.799 0.676
.x8 0.488 0.074 6.573 0.000 0.488 0.477
.x9 0.566 0.071 8.003 0.000 0.566 0.558
f1 1.000 1.000 1.000
f2 1.000 1.000 1.000
f3 1.000 1.000 1.000
Chi-square statistic is significant
Request to modify the index. They are ordered from highest to lowest. By requesting power = TRUEand setting increments SSV application method. delta = .4, Standard load factor means that if the load factor load factor and the model is greater than .4 missing. By delta = .1default, . According to SSV proposal, which is sufficient to resolve the error. Therefore, I choose to use only as an output-related errors.
lhs op rhs mi epc sepc.all delta ncp power decision
30 f1 =~ x9 36.411 0.519 0.515 0.1 1.351 0.213 **(m)**
76 x7 ~~ x8 34.145 0.536 0.488 0.1 1.187 0.193 **(m)**
28 f1 =~ x7 18.631 -0.380 -0.349 0.1 1.294 0.206 **(m)**
78 x8 ~~ x9 14.946 -0.423 -0.415 0.1 0.835 0.150 **(m)**
33 f2 =~ x3 9.151 -0.269 -0.238 0.1 1.266 0.203 **(m)**
55 x2 ~~ x7 8.918 -0.183 -0.143 0.1 2.671 0.373 **(m)**
31 f2 =~ x1 8.903 0.347 0.297 0.1 0.741 0.138 **(m)**
51 x2 ~~ x3 8.532 0.218 0.164 0.1 1.791 0.268 **(m)**
59 x3 ~~ x5 7.858 -0.130 -0.089 0.1 4.643 0.577 **(m)**
26 f1 =~ x5 7.441 -0.189 -0.147 0.1 2.087 0.303 **(m)**
50 x1 ~~ x9 7.335 0.138 0.117 0.1 3.858 0.502 **(m)**
65 x4 ~~ x6 6.221 -0.235 -0.185 0.1 1.128 0.186 **(m)**
66 x4 ~~ x7 5.920 0.098 0.078 0.1 6.141 0.698 **(m)**
48 x1 ~~ x7 5.420 -0.129 -0.102 0.1 3.251 0.438 **(m)**
77 x7 ~~ x9 5.183 -0.187 -0.170 0.1 1.487 0.230 **(m)**
36 f2 =~ x9 4.796 0.137 0.136 0.1 2.557 0.359 **(m)**
29 f1 =~ x8 4.295 -0.189 -0.187 0.1 1.199 0.195 **(m)**
63 x3 ~~ x9 4.126 0.102 0.089 0.1 3.993 0.515 **(m)**
67 x4 ~~ x8 3.805 -0.069 -0.059 0.1 7.975 0.806 (nm)
43 x1 ~~ x2 3.606 -0.184 -0.134 0.1 1.068 0.178 (i)
45 x1 ~~ x4 3.554 0.078 0.058 0.1 5.797 0.673 (i)
35 f2 =~ x8 3.359 -0.120 -0.118 0.1 2.351 0.335 (i)
Check the decision column. x7 and x8 are called incorrectly specified, because the effectiveness of low .193, but MI statistically significant.
However, considering x2 and x7 low power (lhs 55) ,. 373's, MI great. Are there some theories the two projects together? I can explain the relevance of the recommendations it?
Consider x4, and x8 (lhs 67), high-power .806, MI but not significant statistically, so we can conclude that there are no errors specified.
Consider x1 and x4 (lhs 45) ,. 673 a low power, and the MI is not statistically significant, so it is not conclusive.
Now, for a load factor:
lhs op rhs mi epc sepc.all delta ncp power decision
30 f1 =~ x9 36.411 0.519 0.515 0.4 21.620 0.996 *epc:m*
28 f1 =~ x7 18.631 -0.380 -0.349 0.4 20.696 0.995 epc:nm
33 f2 =~ x3 9.151 -0.269 -0.238 0.4 20.258 0.994 epc:nm
31 f2 =~ x1 8.903 0.347 0.297 0.4 11.849 0.931 epc:nm
26 f1 =~ x5 7.441 -0.189 -0.147 0.4 33.388 1.000 epc:nm
36 f2 =~ x9 4.796 0.137 0.136 0.4 40.904 1.000 epc:nm
29 f1 =~ x8 4.295 -0.189 -0.187 0.4 19.178 0.992 epc:nm
35 f2 =~ x8 3.359 -0.120 -0.118 0.4 37.614 1.000 (nm)
27 f1 =~ x6 2.843 0.100 0.092 0.4 45.280 1.000 (nm)
38 f3 =~ x2 1.580 -0.123 -0.105 0.4 16.747 0.984 (nm)
25 f1 =~ x4 1.211 0.069 0.059 0.4 40.867 1.000 (nm)
39 f3 =~ x3 0.716 0.084 0.075 0.4 16.148 0.980 (nm)
42 f3 =~ x6 0.273 0.027 0.025 0.4 58.464 1.000 (nm)
41 f3 =~ x5 0.201 -0.027 -0.021 0.4 43.345 1.000 (nm)
34 f2 =~ x7 0.098 -0.021 -0.019 0.4 36.318 1.000 (nm)
32 f2 =~ x2 0.017 -0.011 -0.010 0.4 21.870 0.997 (nm)
37 f3 =~ x1 0.014 0.015 0.013 0.4 9.700 0.876 (nm)
40 f3 =~ x4 0.003 -0.003 -0.003 0.4 52.995 1.000 (nm)
See the first line, I recommend x9 loaded on f1. High efficiency, MI was significantly higher than .4 and EPC, indicating that it is inappropriate that we should pay attention to some type.
However, the next line is loaded x7 advised me on f1. High efficiency, MI significantly, but the EPC 0.38, less than .4, which indicates that we believe that the extent of this error is not enough to guarantee a specified model needs to be modified. Decided epc: Many proposed changes nm as well.
Then the last group has a higher efficacy, MI but not statistically significant, so we can conclude that there are no errors specified.
SSV use 75%, which is the default setting lavaan, but can be used flexibly.
Please note that you can only change once the model. EPC and MI is calculated under the assumption that other parameters are substantially correct, and therefore, the above-described method steps are performed once changes.
I believe this is the recommended method SSV, following this approach will make people consider the model in the use of MI, taking into account the statistical capacity to detect errors specified. You can solve all non uncertainty relation (theory use, modification, etc.), and leave a model.
PS: Another approach is the latent variable PLS model path modeling. This is an SEM method OLS regression.
- McNeish, D., An, J. , & Hancock, GR (2017). Latent variables in the model difficult to measure the quality of the relationship between the cutoff and fit indices. "Magazine personality assessment" . https://doi.org/10.1080/00223891.2017.1281286 ↩
- Saris, WE, Satorra, A. , & Van der Veld, WM (2009). Testing structural equation modeling to detect errors or specifications? Structural Equation Modeling: Multidisciplinary Journal, 16 (4), 561-582. https://doi.org/10.1080/10705510903203433 ↩
If you have any questions, please leave a comment below.
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