Modification Indices in CFA

[Emma Mills]

Hi, 

I would really appreciate some help...

I'm carrying out confirmatory factor analyses using lavaan and when looking at my one factor solution, my value for RMSEA is just slightly higher than I would like. Therefore I want to look at the modification indices to see which item to remove. I have read that I should be looking at the indices that have =~ as opposed to ~~, but I don't have these in my output (see below)

Is this because it is only one factor? How should I modify my model based on the below:

modificationindices(TRCFA2, sort=TRUE)

     lhs op    rhs     mi mi.scaled    epc sepc.lv sepc.all sepc.nox

72 Post17 ~~ Post18 55.024    36.944  0.073   0.073    0.098    0.098

33  Post1 ~~  Post4 51.355    34.481  0.058   0.058    0.101    0.101

57 Post14 ~~ Post15 32.466    21.798  0.041   0.041    0.070    0.070

51 Post13 ~~ Post15 19.752    13.262 -0.035  -0.035   -0.060   -0.060

41  Post1 ~~ Post20 19.506    13.097  0.035   0.035    0.051    0.051

68 Post16 ~~ Post17 19.220    12.905  0.062   0.062    0.076    0.076

50 Post13 ~~ Post14 18.387    12.345  0.034   0.034    0.059    0.059

77 Post19 ~~ Post20 16.935    11.371  0.035   0.035    0.057    0.057

43  Post4 ~~ Post14 16.005    10.746 -0.032  -0.032   -0.056   -0.056

52 Post13 ~~ Post16 15.069    10.118 -0.043  -0.043   -0.065   -0.065

74 Post17 ~~ Post20 14.704     9.873 -0.042  -0.042   -0.050   -0.050

71 Post16 ~~ Post20 13.584     9.121 -0.038  -0.038   -0.051   -0.051

38  Post1 ~~ Post17 13.103     8.798 -0.038  -0.038   -0.051   -0.051

69 Post16 ~~ Post18 12.297     8.256  0.033   0.033    0.049    0.049

46  Post4 ~~ Post17 11.522     7.736 -0.038  -0.038   -0.054   -0.054

35  Post1 ~~ Post14 10.504     7.053 -0.024  -0.024   -0.041   -0.041

36  Post1 ~~ Post15  8.740     5.868 -0.022  -0.022   -0.036   -0.036

58 Post14 ~~ Post16  8.076     5.423 -0.028  -0.028   -0.043   -0.043

48  Post4 ~~ Post19  5.874     3.944 -0.021  -0.021   -0.042   -0.042

42  Post4 ~~ Post13  5.864     3.937  0.021   0.021    0.037    0.037

63 Post15 ~~ Post16  5.705     3.831  0.023   0.023    0.035    0.035

66 Post15 ~~ Post19  5.336     3.583 -0.018  -0.018   -0.034   -0.034

75 Post18 ~~ Post19  4.744     3.185 -0.017  -0.017   -0.031   -0.031

39  Post1 ~~ Post18  4.605     3.092 -0.015  -0.015   -0.025   -0.025

54 Post13 ~~ Post18  4.193     2.815 -0.016  -0.016   -0.026   -0.026

65 Post15 ~~ Post18  3.813     2.560  0.014   0.014    0.023    0.023

60 Post14 ~~ Post18  3.769     2.531 -0.014  -0.014   -0.023   -0.023

45  Post4 ~~ Post16  3.487     2.341  0.020   0.020    0.032    0.032

55 Post13 ~~ Post19  3.155     2.118  0.016   0.016    0.030    0.030

76 Post18 ~~ Post20  2.946     1.978 -0.013  -0.013   -0.019   -0.019

53 Post13 ~~ Post17  2.719     1.825  0.019   0.019    0.026    0.026

62 Post14 ~~ Post20  2.596     1.743  0.012   0.012    0.019    0.019

40  Post1 ~~ Post19  1.809     1.215  0.011   0.011    0.020    0.020

59 Post14 ~~ Post17  1.166     0.783 -0.011  -0.011   -0.015   -0.015

49  Post4 ~~ Post20  1.146     0.770 -0.009  -0.009   -0.014   -0.014

47  Post4 ~~ Post18  1.120     0.752 -0.008  -0.008   -0.014   -0.014

67 Post15 ~~ Post20  0.869     0.584 -0.007  -0.007   -0.011   -0.011

70 Post16 ~~ Post19  0.470     0.316 -0.008  -0.008   -0.013   -0.013

64 Post15 ~~ Post17  0.275     0.184 -0.005  -0.005   -0.007   -0.007

56 Post13 ~~ Post20  0.207     0.139  0.004   0.004    0.006    0.006

37  Post1 ~~ Post16  0.193     0.130 -0.004  -0.004   -0.007   -0.007

73 Post17 ~~ Post19  0.081     0.055 -0.003  -0.003   -0.005   -0.005

34  Post1 ~~ Post13  0.081     0.055  0.002   0.002    0.004    0.004

61 Post14 ~~ Post19  0.047     0.032 -0.002  -0.002   -0.003   -0.003

44  Post4 ~~ Post15  0.046     0.031  0.002   0.002    0.003    0.003

Thanks in advance, 

Emma.

[김계수]

Dear Emma Mills,

You know that formula type ~~ is residual covariance between one variable(latent variable) and other variable(latent variable). If you want to use modification model strategy, please covariate Post17 ~~ Post1. Becasue MI can be decrease much chi-square in this case. But you should confirm your data specification and strong theorethical foundation.

     lhs op    rhs     mi mi.scaled    epc sepc.lv sepc.all sepc.nox

72 Post17 ~~ Post18 55.024    36.944  0.073   0.073    0.098    0.098

Best regard,

2016년 8월 27일 토요일 오후 9시 18분 43초 UTC+9, Emma Mills 님의 말:

[Emma Mills]

Hi, Thanks for your prompt response!

I'm not sure I fully understand though - should I remove Post 17 from my model and re-run to see if this improves the model fit indices (including the chi square value)?  I'm not sure what you mean by '  please covariate Post17 ~~ Post1'

Thanks

Emma.

[김계수]

 Please add Post17 ~~ Post1 in yourmodel equation. And then re-run. After that you can find your model improvement.

Thanks,

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세명대학교 대외협력처장/국제교육원장/경영학과 교수
Dean for Int'l Affairs of Sermyung Univ/
Department of Business Administration, Semyung University
#65 Semyungro, Jechon Chungbuk 390-711, Korea(ROK)
http://cafe.daum.net/semstatistics

[phone] +82-43-649-1242 (office) or 010-9428-6768 (cell)
[fax] +82-43-649-1242 (office)
[e-mail] gs...@semyung.ac.kr
           seml...@gmail.com

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[Oleksii Shestakovskyi]

Hi all,

it seems to me, that here you should ad a covariation Post17 ~~ Post18

Emma,

if you want to drop an item instead of  adding error covariance, you can just drop the item with a low (lower than +/-0.4 usually) loading.

But again, as our colleague has written before, you should have theoretical explanations for that.

Second, after dropping an item, your new model won't be comparable with previous one. You cannot directly compare chi-squares and measures of fit.

Best,

Oleksii Shestakovskyi

independent researcher, Ukraine

 
субота, 27 серпня 2016 р. 15:18:43 UTC+3 користувач Emma Mills написав:

[kma...@aol.com]

Emma,
I would like to offer a little different perspective on this.  Modification indices are limited to parameters included in the model specification but fixed (which is different from not even being represented in the model specification).  Looking over your modification indicies, there appear to be groups of 3 or more items that all suggest greater covariation than allowed by your one-factor model.  For example, items 13, 14 and 15 appear to follow this pattern.  So, you should also consider the possibility that you have too few factors and that certain clusters of items should load on separate factors.  The resulting multi-factor model may offer a more useful substantive description of your items than a one-factor model with many free covariances between item uniquenesses.  You should closely examine the residuals to look for patterns in the ill fit to help supplement your use of modification indices.

Keith
------------------------
Keith A. Markus
John Jay College of Criminal Justice, CUNY
http://jjcweb.jjay.cuny.edu/kmarkus
Frontiers of Test Validity Theory: Measurement, Causation and Meaning.
http://www.routledge.com/books/details/9781841692203/