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Title: E-mail: rejoice@zeta.mcu.edu.tw


1
????????????(1)
??? ??????????????
?????
98????????
E-mail rejoice_at_zeta.mcu.edu.tw
2
??
3
???????,??????(Structural Equation Modeling,
SEM)????????????,???????????????????SEM???????????
?????????????????????????????????????????(Confirma
tory Factor Analysis, CFA)??????????,?????????????
????????????????,?????????????,???????????????????
?,???????????????
4
???????(????)
???????
5
?????SIWB-12
?????Dr. Frey???????????????? Hello
Rejoice, Thank you for your email. Yes, you may
use the SIWB. It is in the public domain. Please
reference us in your research and we'd be happy
to see any results of your study! Best of
luck, Bruce
Bruce Frey, Ph.D. Assistant Professor,
Psychology and Research in Education University
of Kansas 1122 West Campus Road, Room
643 Lawrence, KS 66045 785-864-9706
Office 785-864-3820 FAX bfrey_at_ku.edu

Source ???(2006)?????????????????????????,???
??????????
6
  • ????(existential intelligence)????????????????????
    ???????????????????????????(well-being)??????????
    ???????????,???????????Frey, Daaleman,
    Peyton(2005)?????????????,????????,???????,???????
    ???,?????????,???????????????,???????????,????
  • ???????????????????,????????
  • ??????????
  • (2) ?????????????,??????????????
  • ???,??????????????

Source 1.???(2006)?????????????????????????,??
???????????
2. Freg, B. B., Daaleman P. T., Peyton V.
(2005)Measuring a dimension of spiritually
for health research. Research on aging , 27,
556-577.
7
???? (????????????,?????????) 1 - ?????? 6 - ????? ???? (????????????,?????????) 1 - ?????? 6 - ????? ???? (????????????,?????????) 1 - ?????? 6 - ????? ???? (????????????,?????????) 1 - ?????? 6 - ????? ???? (????????????,?????????) 1 - ?????? 6 - ????? ???? (????????????,?????????) 1 - ?????? 6 - ????? ???? (????????????,?????????) 1 - ?????? 6 - ?????
1. ???????????? 1 2 3 4 5 6
2. ???????????,?????????? ??????? 1 2 3 4 5 6
3. ???????????? 1 2 3 4 5 6
4. ?????????????? 1 2 3 4 5 6
5. ?????????????? 1 2 3 4 5 6
6. ????????????? 1 2 3 4 5 6
7. ???????,??????? 1 2 3 4 5 6
8. ?????????????? 1 2 3 4 5 6
9. ???????????????? 1 2 3 4 5 6
10. ??????????? 1 2 3 4 5 6
Source ???(2006)?????????????????????????,???
??????????
8
????-??
9
KMO? ????
KMO lt 0.5 ????
0.5 KMO lt 0.6 ??????
0.6 KMO lt 0.7 ????
0.7 KMO lt 0.8 ??????
0.8 KMO lt 0.9 ????
KMO 0.9 ??????
10
(No Transcript)
11
(No Transcript)
12
Pattern Matrixa Pattern Matrixa Pattern Matrixa
Factor Factor
1 2
exist1 .535 .067
exist2 .685 -.011
exist3 .756 -.005
exist4 .865 -.076
exist5 .821 .011
exist6 .674 .147
exist7 .104 .726
exist8 .055 .657
exist9 -.052 .952
exist10 -.036 .876
13
????????? ???
14
??????
For LISREL
15
exist1 exist2 exist3 exist4 exist5 exist6 exist7 exist8 exist9 exist10
exist1 1.00
exist2 .55 1.00
exist3 .46 .56 1.00
exist4 .42 .49 .65 1.00
exist5 .41 .51 .58 .72 1.00
exist6 .39 .48 .50 .63 .73 1.00
exist7 .30 .34 .37 .37 .45 .49 1.00
exist8 .34 .29 .33 .32 .32 .35 .53 1.00
exist9 .32 .30 .36 .35 .42 .47 .71 .66 1.00
exist10 .29 .30 .35 .34 .37 .43 .69 .58 .78 1.00
16
??CFA
?????
17
(No Transcript)
18
Observed Variables exist1 exist2 exist3 exist4
exist5 exist6 exist7 exist8 exist9
exist10 Correlation Matrix 1.00 .55
1.00 .46 .56 1.00 .42 .49 .65
1.00 .41 .51 .58 .72 1.00 .39 .48 .50
.63 .73 1.00 .30 .34 .37 .37 .45 .49
1.00 .34 .29 .33 .32 .32 .35 .53 1.00 .32
.30 .36 .35 .42 .47 .71 .66 1.00 .29 .30 .35 .34
.37 .43 .69 .58 .78 1.00 Sample Size
673 Latent Variables LIFEMEAN SELFEFFC Relationsh
ips exist1 exist2 exist3 exist4 exist5 exist6
LIFEMEAN exist7 exist8 exist9 exist10
SELFEFFC Number of Decimals 3 Wide
Print Print Residuals path diagram LISREL Output
SE TV RS EF MI SS SC WP End of Problem
19
????
20
???????!!!
?????
????
21
???????????(Structural Equation Modeling,
SEM)????,???????????SEM????(1)?????(2)??????????SE
M?????????????????,??????????????????,????????????
??,??????????????????????????????????(???)??????(?
??,2006)??????Hair, Black, Babin,
Anderson(2010)???6????????????,????6???
??1?????? ??2????????? ??3???????????
??4???????? ??5?????? ??6???????? ????SEM??
????,???????????????(2006)????7?????????
??1???????? ??2??????????????
??3????????????????? ??4??????(????????)
??5?????? ??6??????? ??7???????
??????
22
??1
23
  • When a model has scales borrowed from various
    sources reporting other research, a pretest using
    respondents similar to those from the population
    to be studies is recommended to screen items for
    appropriateness.
  • Pairwise deletion of missing cases (all-available
    approach) is a good alternative handling missing
    data when the amount of missing data is less
    than 10 and the sample size is 250 or more.
  • Covariance matrices provide the researcher with
    far more flexibility due to the relatively
    greater information content thy contain and are
    the recommended for m of input to SEM models.
  • The minimum sample size for a particular SEM
    model depends on several factors, including the
    model complexity and the common communalities
    (average variance extracted among items) in each
    factor
  • SEM models containing five or few constructs,
    each with more than three items (observed
    variables), and with high item communalities (0.6
    or higher) , can be adequately estimated with
    samples as small as 100 to 150.
  • When the number of factors greater than six, some
    of which have fewer than three measured items as
    indicators, and multiple low communalities are
    present, sample size requirements may exceed 500.
  • No matter the modeling approach, the sample size
    must be sufficient to allow the model to run,
    but, more important, it must adequately represent
    the population of interest.

24
SEM????????? (OLD) SEM????????? (OLD) SEM????????? (OLD)
?? ???? ????
? ? ? ? ? ? ??? ????????????
? ? ? ? ? ? GFI ??0.90,??????????????????????
? ? ? ? ? ? AGFI ??0.90,?????????????????????
? ? ? ? ? ? SRMR ??0.05,????????????
? ? ? ? ? ? RMSEA ??0.05,??0.05??????0.05?0.08??????0.08?0.10????????0.10???????
? ? ? ? ? ? ECVI ?????ECVI???????????ECVI?
? ? ? ? ? ? NFI ??0.90,?????????????????????????????????
? ? ? ? ? ? NNFI ??0.90,????????????????
? ? ? ? ? ? IFI ??0.90,??NNFI??????????NFI????
? ? ? ? ? ? CFI ??0.90,??????????????,??????
? ? ? ? ? ? RFI ??0.90?
? ? ? ? ? ? PNFI ??0.50?
? ? ? ? ? ? PGFI ??0.50,???????????,???SEM??????????
? ? ? ? ? ? AIC ?????AIC????????????AIC??
? ? ? ? ? ? CN ????????,?CNgt200?,???????????????????
25
Goodness of Fit Statistics
Degrees of Freedom 34
Minimum Fit Function Chi-Square 265.883 (P
0.0) Normal Theory Weighted Least Squares
Chi-Square 283.559 (P 0.0)
Estimated Non-centrality Parameter (NCP)
249.559 90 Percent Confidence Interval
for NCP (199.536 307.058)
Minimum Fit Function Value 0.396
Population Discrepancy Function Value (F0)
0.371 90 Percent Confidence
Interval for F0 (0.297 0.457)
Root Mean Square Error of Approximation (RMSEA)
0.105 90 Percent Confidence Interval
for RMSEA (0.0935 0.116)
P-Value for Test of Close Fit (RMSEA lt 0.05)
0.000 Expected
Cross-Validation Index (ECVI) 0.484
90 Percent Confidence Interval for ECVI (0.410
0.570) ECVI for
Saturated Model 0.164
ECVI for Independence Model 10.317
Chi-Square for Independence Model with 45 Degrees
of Freedom 6912.998
Independence AIC 6932.998
Model AIC 325.559
Saturated AIC 110.000
Independence CAIC 6988.116
Model CAIC 441.306
Saturated CAIC 413.146
Normed Fit Index (NFI)
0.962 Non-Normed Fit Index
(NNFI) 0.955 Parsimony
Normed Fit Index (PNFI) 0.726
Comparative Fit Index (CFI) 0.966
Incremental Fit Index (IFI)
0.966 Relative Fit Index
(RFI) 0.949
Critical N (CN) 142.691
Root Mean Square Residual (RMR) 0.0512
Standardized RMR 0.0512
Goodness of Fit Index (GFI)
0.922 Adjusted Goodness of Fit
Index (AGFI) 0.874 Parsimony
Goodness of Fit Index (PGFI) 0.570
????
26
Summary Statistics for Standardized Residuals
Smallest Standardized Residual -5.828
Median Standardized Residual 0.000 Largest
Standardized Residual 8.564 Stemleaf
Plot - 48432 - 259865500 -
0999549863200000000000 08112346888
21001119 4716 60 86 Largest
Negative Standardized Residuals Residual for
exist4 and exist2 -2.829 Residual for
exist5 and exist1 -4.415 Residual for
exist5 and exist2 -3.530 Residual for
exist5 and exist3 -4.213 Residual for
exist6 and exist3 -5.828 Residual for
exist9 and exist4 -4.270 Residual for
exist10 and exist4 -2.942 Largest Positive
Standardized Residuals Residual for exist2 and
exist1 8.564 Residual for exist3 and
exist1 3.070 Residual for exist3 and
exist2 5.127 Residual for exist4 and
exist3 4.717 Residual for exist5 and
exist4 2.991 Residual for exist6 and
exist5 7.028 Residual for exist7 and
exist5 2.986 Residual for exist7 and
exist6 5.620 Residual for exist8 and
exist1 3.864 Residual for exist9 and
exist6 3.098 Residual for exist9 and
exist8 3.091
27
????1
28
Goodness of Fit Statistics
Degrees of Freedom 26
Minimum Fit Function Chi-Square 166.877 (P
0.0) Normal Theory Weighted Least Squares
Chi-Square 168.911 (P 0.0)
Estimated Non-centrality Parameter (NCP)
142.911 90 Percent Confidence Interval
for NCP (105.520 187.801)
Minimum Fit Function Value 0.248
Population Discrepancy Function Value (F0)
0.213 90 Percent Confidence
Interval for F0 (0.157 0.279)
Root Mean Square Error of Approximation (RMSEA)
0.0904 90 Percent Confidence Interval
for RMSEA (0.0777 0.104)
P-Value for Test of Close Fit (RMSEA lt 0.05)
0.000 Expected
Cross-Validation Index (ECVI) 0.308
90 Percent Confidence Interval for ECVI (0.252
0.375) ECVI for
Saturated Model 0.134
ECVI for Independence Model 8.911
Chi-Square for Independence Model with 36 Degrees
of Freedom 5970.317
Independence AIC 5988.317
Model AIC 206.911
Saturated AIC 90.000
Independence CAIC 6037.923
Model CAIC 311.634
Saturated CAIC 338.029
Normed Fit Index (NFI)
0.972 Non-Normed Fit Index
(NNFI) 0.967 Parsimony
Normed Fit Index (PNFI) 0.702
Comparative Fit Index (CFI) 0.976
Incremental Fit Index (IFI)
0.976 Relative Fit Index
(RFI) 0.961
Critical N (CN) 184.796
Root Mean Square Residual (RMR) 0.0424
Standardized RMR 0.0424
Goodness of Fit Index (GFI)
0.947 Adjusted Goodness of Fit
Index (AGFI) 0.908 Parsimony
Goodness of Fit Index (PGFI) 0.547
????1
29
Summary Statistics for Standardized Residuals
Smallest Standardized Residual -5.483
Median Standardized Residual 0.000 Largest
Standardized Residual 6.257 Stemleaf
Plot - 4541 - 218755 - 099740073200000000
0 0113023578 2012022 4567 63
Largest Negative Standardized Residuals Residual
for exist5 and exist3 -4.363 Residual for
exist6 and exist3 -5.483 Residual for
exist6 and exist4 -3.055 Residual for
exist9 and exist4 -4.076 Residual for
exist10 and exist4 -2.766 Residual for
exist10 and exist5 -2.663 Largest Positive
Standardized Residuals Residual for exist3 and
exist2 6.257 Residual for exist4 and
exist3 5.505 Residual for exist6 and
exist5 5.629 Residual for exist7 and
exist5 2.969 Residual for exist7 and
exist6 5.688 Residual for exist9 and
exist6 3.180 Residual for exist9 and
exist8 3.175
30
????2 ?????
31
Goodness of Fit Statistics
Degrees of Freedom 19
Minimum Fit Function Chi-Square 72.824 (P
0.000) Normal Theory Weighted Least
Squares Chi-Square 71.657 (P 0.000)
Estimated Non-centrality Parameter (NCP)
52.657 90 Percent Confidence Interval
for NCP (30.413 82.476)
Minimum Fit Function Value 0.108
Population Discrepancy Function Value (F0)
0.0784 90 Percent Confidence
Interval for F0 (0.0453 0.123)
Root Mean Square Error of Approximation (RMSEA)
0.0642 90 Percent Confidence Interval
for RMSEA (0.0488 0.0804)
P-Value for Test of Close Fit (RMSEA lt 0.05)
0.0637 Expected
Cross-Validation Index (ECVI) 0.157
90 Percent Confidence Interval for ECVI (0.124
0.202) ECVI for
Saturated Model 0.107
ECVI for Independence Model 7.088
Chi-Square for Independence Model with 28 Degrees
of Freedom 4747.008
Independence AIC 4763.008
Model AIC 105.657
Saturated AIC 72.000
Independence CAIC 4807.102
Model CAIC 199.357
Saturated CAIC 270.423
Normed Fit Index (NFI)
0.985 Non-Normed Fit Index
(NNFI) 0.983 Parsimony
Normed Fit Index (PNFI) 0.668
Comparative Fit Index (CFI) 0.989
Incremental Fit Index (IFI)
0.989 Relative Fit Index
(RFI) 0.977
Critical N (CN) 334.959
Root Mean Square Residual (RMR) 0.0359
Standardized RMR 0.0359
Goodness of Fit Index (GFI)
0.974 Adjusted Goodness of Fit
Index (AGFI) 0.951 Parsimony
Goodness of Fit Index (PGFI) 0.514
????2 ?????
32
????????
33
???????
34
????
35
N lt 250 N lt 250 N lt 250 N gt 250 N gt 250 N gt 250
m?? mlt12 12ltmlt30 mgt30 mlt12 12ltmlt30 mgt30
??? ????? ??????? ???? ?????????? ???? ????
CFI ? TLI gt 0.97 gt0.95 gt0.92 gt0.95 gt0.92 gt0.9
RNI ?????????? gt0.95 gt0.92 gt0.95,????Ngt1000 gt0.92,????Ngt1000 gt0.9,????Ngt1000
SRMR ????,?????? lt0.08,?CFIgt0.95 lt0.09,?CFIgt0.92 ????,?????? lt0.08,?CFIgt0.92 lt0.08,?CFIgt0.92
RMSEA lt0.08,?CFIgt0.97 lt0.08,?CFIgt0.95 lt0.08,?CFIgt0.95 lt0.07,?CFIgt0.97 lt0.07,?CFIgt0.92 lt0.07,?CFIgt0.90
36
Goodness of Fit Statistics
Degrees of Freedom 19
Minimum Fit Function Chi-Square 72.824 (P
0.000) Normal Theory Weighted Least
Squares Chi-Square 71.657 (P 0.000)
Estimated Non-centrality Parameter (NCP)
52.657 90 Percent Confidence Interval
for NCP (30.413 82.476)
Minimum Fit Function Value 0.108
Population Discrepancy Function Value (F0)
0.0784 90 Percent Confidence
Interval for F0 (0.0453 0.123)
Root Mean Square Error of Approximation (RMSEA)
0.0642 90 Percent Confidence Interval
for RMSEA (0.0488 0.0804)
P-Value for Test of Close Fit (RMSEA lt 0.05)
0.0637 Expected
Cross-Validation Index (ECVI) 0.157
90 Percent Confidence Interval for ECVI (0.124
0.202) ECVI for
Saturated Model 0.107
ECVI for Independence Model 7.088
Chi-Square for Independence Model with 28 Degrees
of Freedom 4747.008
Independence AIC 4763.008
Model AIC 105.657
Saturated AIC 72.000
Independence CAIC 4807.102
Model CAIC 199.357
Saturated CAIC 270.423
Normed Fit Index (NFI)
0.985 Non-Normed Fit Index
(NNFI) 0.983 Parsimony
Normed Fit Index (PNFI) 0.668
Comparative Fit Index (CFI) 0.989
Incremental Fit Index (IFI)
0.989 Relative Fit Index
(RFI) 0.977
Critical N (CN) 334.959
Root Mean Square Residual (RMR) 0.0359
Standardized RMR 0.0359
Goodness of Fit Index (GFI)
0.974 Adjusted Goodness of Fit
Index (AGFI) 0.951 Parsimony
Goodness of Fit Index (PGFI) 0.514
????2 ?????
37
????2 ????
38
??SEM
??LISREL
39
Observed Variables exist1 exist2 exist3 exist4
exist5 exist6 exist7 exist8 exist9
exist10 Correlation Matrix 1.00 .55
1.00 .46 .56 1.00 .42 .49 .65
1.00 .41 .51 .58 .72 1.00 .39 .48 .50
.63 .73 1.00 .30 .34 .37 .37 .45 .49
1.00 .34 .29 .33 .32 .32 .35 .53 1.00 .32
.30 .36 .35 .42 .47 .71 .66 1.00 .29 .30 .35 .34
.37 .43 .69 .58 .78 1.00 Sample Size
673 Latent Variables LIFEMEAN SELFEFFC Relationsh
ips exist1 exist2 exist3 exist4 exist5 exist6
LIFEMEAN exist7 exist8 exist9 exist10
SELFEFFC SELFEFFC LIFEMEAN Number of Decimals
3 Wide Print Print Residuals path
diagram LISREL Output SE TV RS EF MI SS SC WP End
of Problem
40
SELFEFFC LIFEMEAN
CFA ? SEM
41
SEM ????
42
Goodness of Fit Statistics
Degrees of Freedom 34
Minimum Fit Function Chi-Square 265.883 (P
0.0) Normal Theory Weighted Least Squares
Chi-Square 283.559 (P 0.0)
Estimated Non-centrality Parameter (NCP)
249.559 90 Percent Confidence Interval
for NCP (199.536 307.058)
Minimum Fit Function Value 0.396
Population Discrepancy Function Value (F0)
0.371 90 Percent Confidence
Interval for F0 (0.297 0.457)
Root Mean Square Error of Approximation (RMSEA)
0.105 90 Percent Confidence Interval
for RMSEA (0.0935 0.116)
P-Value for Test of Close Fit (RMSEA lt 0.05)
0.000 Expected
Cross-Validation Index (ECVI) 0.484
90 Percent Confidence Interval for ECVI (0.410
0.570) ECVI for
Saturated Model 0.164
ECVI for Independence Model 10.317
Chi-Square for Independence Model with 45 Degrees
of Freedom 6912.998
Independence AIC 6932.998
Model AIC 325.559
Saturated AIC 110.000
Independence CAIC 6988.116
Model CAIC 441.306
Saturated CAIC 413.146
Normed Fit Index (NFI)
0.962 Non-Normed Fit Index
(NNFI) 0.955 Parsimony
Normed Fit Index (PNFI) 0.726
Comparative Fit Index (CFI) 0.966
Incremental Fit Index (IFI)
0.966 Relative Fit Index
(RFI) 0.949
Critical N (CN) 142.691
Root Mean Square Residual (RMR) 0.0512
Standardized RMR 0.0512
Goodness of Fit Index (GFI)
0.922 Adjusted Goodness of Fit
Index (AGFI) 0.874 Parsimony
Goodness of Fit Index (PGFI) 0.570
Goodness of Fit Statistics
Degrees of Freedom 34
Minimum Fit Function Chi-Square 265.883 (P
0.0) Normal Theory Weighted Least Squares
Chi-Square 283.559 (P 0.0)
Estimated Non-centrality Parameter (NCP)
249.559 90 Percent Confidence Interval
for NCP (199.536 307.057)
Minimum Fit Function Value 0.396
Population Discrepancy Function Value (F0)
0.371 90 Percent Confidence
Interval for F0 (0.297 0.457)
Root Mean Square Error of Approximation (RMSEA)
0.105 90 Percent Confidence Interval
for RMSEA (0.0935 0.116)
P-Value for Test of Close Fit (RMSEA lt 0.05)
0.000 Expected
Cross-Validation Index (ECVI) 0.484
90 Percent Confidence Interval for ECVI (0.410
0.570) ECVI for
Saturated Model 0.164
ECVI for Independence Model 10.317
Chi-Square for Independence Model with 45 Degrees
of Freedom 6912.998
Independence AIC 6932.998
Model AIC 325.559
Saturated AIC 110.000
Independence CAIC 6988.116
Model CAIC 441.305
Saturated CAIC 413.146
Normed Fit Index (NFI)
0.962 Non-Normed Fit Index
(NNFI) 0.955 Parsimony
Normed Fit Index (PNFI) 0.726
Comparative Fit Index (CFI) 0.966
Incremental Fit Index (IFI)
0.966 Relative Fit Index
(RFI) 0.949
Critical N (CN) 142.691
Root Mean Square Residual (RMR) 0.0512
Standardized RMR 0.0512
Goodness of Fit Index (GFI)
0.922 Adjusted Goodness of Fit
Index (AGFI) 0.874 Parsimony
Goodness of Fit Index (PGFI) 0.570
SEM
CFA
43
??????
CFA SEM(????????)
44
??2
45
  • As model become more complex, the likelihood of
    alternative models with equivalent fit increases.
  • Multiple fit indices should be used to assess a
    models goodness-of-fit and should include
  • The ?2 value and the associated df.
  • One absolute fit index (i.e., GFI, RMSEA, or SRMR)
  • One incremental fit index(i.e., CFI or TLI)
  • One goodness-of-fit index(GFI, CFI, TLI, etc.)
  • One badness-of-fit index (RMSEA, SRMR, etc.)
  • No single magic value for the fit indices
    separates good from poor models, and it is not
    practical to apply a single set of cutoff rules
    to all measurement models and for that matter to
    all SEM models of any type.
  • The quality of fit depend heavily on model
    characteristics including sample size and model
    complexity
  • Simple models with small samples should be held
    to strict fit standards, even an insignificant
    p-value for a simple model may not be meaningful.
  • More complex models with large samples should be
    held to the same strict standards, and so when
    samples are large and the model contains a large
    number of measured variables and parameter
    estimates, cutoff values of 0.95 on key GOF
    measures are unrealistic.
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