summaryGOF: Goodness-of-Fit indexes in structural equation models for...
In semGOF: Goodness-of-fit indexes for structural equation models
Description
Usage
Arguments
Details
Warning
Author(s)
References
See Also
Examples
Description
summaryGOF computes fourteen Goodness–of–Fit indexes in addiction to the output of sem (Fox, Byrnes, Culbertson, Friendly, Kramer & Monette; 2011).
Usage
1
summaryGOF(object, digits = 5, ...)
Arguments
object
an object of class sem returned by the sem function (see Examples below).
digits
number of digits for printed output.
...
additional arguments affecting the summary produced (see summary).
Details
The goodness of fit indexes calculated in semGOF:
- ICOMP
Information Complexity (Bozdogan, 1990)
- Fml
Fit Function of maximum likelihood (Long, 1986).
- d
Estimate of minimized population discrepancy function (McDonald, 1989).
- Mc
McDonald's Centrality Index (McDonald, 1989).
- RNI
Relative Noncentrality Index (Bentler, 1990).
- IFI
Incremental Fit Index (Bollen, 1989).
- chisq.df
Chi-square/df ratio (Marsh & al., 1988).
- CAK
Rescaled version of AIC (Cudeck and Browne, 1983).
- CSK
Information Criterion (Schwartz, 1978).
- CN
Critical N (Hoelter, 1983), (Hu & Bentler, 1999).
- Gamma.hat
Gamma hat (Steiger, 1989), (Hu & Bentler, 1999).
- BL86
Bollen's Fit Index (Bollen, 1986).
- W
Wheaton Index (Wheaton et al., 1977).
- ECVI
Expected Cross Validation Index (Browne & Cudeck, 1992).
Warning
semGOF must be used with sem.
Author(s)
Bertossi Elena bertossielena@gmail.com
References
Bentler, P. M. (1990)
Comparative fit indexes in structural equation models.
Psychological Bulletin
107:238–246.
Bollen, K. A. (1986)
Sample size and Bentler and Bonnett's nonnormed fit index.
Psychometrika
51:375–377.
Bollen, K. A. (1989)
A new incremental fit index for general structural equation models.
Sociological Methods and Research
17:303–316.
Bozdogan, H. (1990)
Akaike's criterion and recent developments in information complexity.
Journal of Mathematical Psychology
44:62–91.
Browne, M. W., Cudeck, R. (1992)
Alternative ways of assessing model fit.
Sociological Methods and Research
21:230–258.
Cudeck, R., Browne, M. W.(1983)
Cross–validation of covariance structure.
Multivariate Behavioral Research
18:147–167.
John Fox, Jarrett Byrnes, with contributions from Michael Culbertson,
Michael Friendly, Adam Kramer and Georges Monette. (2011)
sem: Structural Equation Models. R package version 2.1-1.
http://CRAN.R-project.org/package=sem
Fox, L. (2006)
Structural equation modeling with the sem package in R.
Structural equation modeling
13:465–486.
Hoelter, J. W.(1983)
The analysis of covariance structure: goodness of fit indexes.
Sociological Methods and Research
11:325–344.
Hu, J.,Bentler, P M. (1999)
Cutoff criteria for fit indexes in covariance structure analysis: conventional criteria versus new alternatives.
Stuctural equation modeling
6:1–55.
Long J. S. (1986)
Confirmatory Factor Analysis.
California, SAGE.
Marsh, H. W., Balla, J. R. McDonald, R. P. (1988)
Goodness–of–fit in confirmatory factor analysis: the effect of sample size.
Psychological Bulletin
3:391–410.
McDonald, R. P. (1989)
An index of goodeness of fit based on noncentrality.
Journal of Classification
6:97–103.
Schwartz, G. (1978)
Estimating the dimantion of the model.
Annals of Statistics
6:461–464.
Venables, W. N. & Ripley, B. D. (2002)
Modern Applied Statistics with S.
Fourth Edition. Springer, New York.
ISBN 0-387-95457-0.
Wheaton, B., Muthen, B., Alwin, D. F., Summers, G. (1977)
Assessing reliability and stability in panel models.
Sociological Methodology
8:84–136.
See Also
Examples
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# The following model has been created with
# six observed endogenous variables,
# two unobserved endogenous variables and
# four unobserved exogenous variables.
S <- matrix(c(
1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0,
0.6321, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0,
0.5932, 0.5881, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0,
0.0965, 0.0987, 0.1564, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0,
0.1785, 0.1256, 0.1124, 0.4567, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0,
0.2135, 0.2003, 0.0762, 0.5589, 0.6097, 1.0000, 0.0000, 0.0000, 0.0000, 0,
0.3875, 0.4011, 0.3211, 0.0134, 0.0189, 0.0556, 1.0000, 0.0000, 0.0000, 0,
0.3569, 0.3989, 0.3301, 0.1323, 0.1036, 0.1132, 0.3215, 1.0000, 0.0000, 0,
0.1034, 0.1201, 0.1010, 0.2981, 0.3265, 0.2920, 0.1092, 0.0981, 1.0000, 0,
0.1324, 0.0622, 0.0123, 0.3056, 0.3525, 0.2661, 0.1234, 0.1207, 0.2221, 1
), ncol=10, byrow=TRUE)
rownames(S) <- c("Y1", "Y2", "Y3", "Y4", "Y5", "Y6",
"CSI1", "CSI2", "CSI3", "CSI4")
colnames(S) <- c("Y1", "Y2", "Y3", "Y4", "Y5", "Y6",
"CSI1", "CSI2", "CSI3", "CSI4")
ram.I <- matrix(c(
# heads to from param start
1, 1, 11, 1, NA, # lam1
1, 2, 11, 0, 0.750,
1, 3, 11, 2, NA, # lam2
1, 4, 12, 3, NA, # lam3
1, 5, 12, 4, NA, # lam4
1, 6, 12, 0, 0.800,
1, 11, 7, 5, NA, # gam1
1, 11, 8, 6, NA, # gam2
1, 12, 9, 7, NA, # gam3
1, 12, 10, 8, NA, # gam4
2, 1, 1, 9, NA, # theta1
2, 2, 2, 10, NA, # theta2
2, 3, 3, 11, NA, # theta3
2, 4, 4, 12, NA, # theta4
2, 5, 5, 13, NA, # theta5
2, 6, 6, 14, NA, # theta6
2, 11, 11, 15, NA, # psi1
2, 12, 12, 16, NA # psi2
), ncol=5, byrow=TRUE)
params.I <- c('lam1', 'lam2', 'lam3', 'lam4', 'gam1', 'gam2',
'gam3', 'gam4', 'theta1', 'theta2', 'theta3',
'theta4', 'theta5', 'theta6', 'psi1', 'psi2')
vars.I <- c('Y1', 'Y2', 'Y3', 'Y4', 'Y5', 'Y6', 'CSI1',
'CSI2', 'CSI3', 'CSI4', 'ETA1', 'ETA2')
sem.I <- sem(ram.I, S, 250, param.names=params.I,
var.names=vars.I, fixed.x=7:10)
summaryGOF(sem.I)
# Goodness-of-Fit indexes of structural equation models for 'sem' package
# ICOMP = -14.964
# Fml = 0.19582
# RNI = 0.97065
# IFI = 0.97133
# chisq.df = 1.6814
# CN = 231.91
# Gamma.hat = 0.98438
# BL86 = 0.89465
# W = 1.6814
# d = 0.079042
# Mc = 0.96125
# CAK = 0.27582
# CSK = 0.41668
# ECVI = 0.40466
semGOF documentation built on May 30, 2017, 3:22 a.m.
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Description Usage Arguments Details Warning Author(s) References See Also Examples
Description
summaryGOF computes fourteen Goodness–of–Fit indexes in addiction to the output of sem (Fox, Byrnes, Culbertson, Friendly, Kramer & Monette; 2011).
Usage
1 | summaryGOF(object, digits = 5, ...)
|
Arguments
object |
an object of class sem returned by the |
digits |
number of digits for printed output. |
... |
additional arguments affecting the summary produced (see |
Details
The goodness of fit indexes calculated in semGOF:
- ICOMP
Information Complexity (Bozdogan, 1990)
- Fml
Fit Function of maximum likelihood (Long, 1986).
- d
Estimate of minimized population discrepancy function (McDonald, 1989).
- Mc
McDonald's Centrality Index (McDonald, 1989).
- RNI
Relative Noncentrality Index (Bentler, 1990).
- IFI
Incremental Fit Index (Bollen, 1989).
- chisq.df
Chi-square/df ratio (Marsh & al., 1988).
- CAK
Rescaled version of AIC (Cudeck and Browne, 1983).
- CSK
Information Criterion (Schwartz, 1978).
- CN
Critical N (Hoelter, 1983), (Hu & Bentler, 1999).
- Gamma.hat
Gamma hat (Steiger, 1989), (Hu & Bentler, 1999).
- BL86
Bollen's Fit Index (Bollen, 1986).
- W
Wheaton Index (Wheaton et al., 1977).
- ECVI
Expected Cross Validation Index (Browne & Cudeck, 1992).
Warning
semGOF must be used with sem.
Author(s)
Bertossi Elena bertossielena@gmail.com
References
Bentler, P. M. (1990) Comparative fit indexes in structural equation models. Psychological Bulletin 107:238–246.
Bollen, K. A. (1986) Sample size and Bentler and Bonnett's nonnormed fit index. Psychometrika 51:375–377.
Bollen, K. A. (1989) A new incremental fit index for general structural equation models. Sociological Methods and Research 17:303–316.
Bozdogan, H. (1990) Akaike's criterion and recent developments in information complexity. Journal of Mathematical Psychology 44:62–91.
Browne, M. W., Cudeck, R. (1992) Alternative ways of assessing model fit. Sociological Methods and Research 21:230–258.
Cudeck, R., Browne, M. W.(1983) Cross–validation of covariance structure. Multivariate Behavioral Research 18:147–167.
John Fox, Jarrett Byrnes, with contributions from Michael Culbertson, Michael Friendly, Adam Kramer and Georges Monette. (2011) sem: Structural Equation Models. R package version 2.1-1. http://CRAN.R-project.org/package=sem
Fox, L. (2006) Structural equation modeling with the sem package in R. Structural equation modeling 13:465–486.
Hoelter, J. W.(1983) The analysis of covariance structure: goodness of fit indexes. Sociological Methods and Research 11:325–344.
Hu, J.,Bentler, P M. (1999) Cutoff criteria for fit indexes in covariance structure analysis: conventional criteria versus new alternatives. Stuctural equation modeling 6:1–55.
Long J. S. (1986) Confirmatory Factor Analysis. California, SAGE.
Marsh, H. W., Balla, J. R. McDonald, R. P. (1988) Goodness–of–fit in confirmatory factor analysis: the effect of sample size. Psychological Bulletin 3:391–410.
McDonald, R. P. (1989) An index of goodeness of fit based on noncentrality. Journal of Classification 6:97–103.
Schwartz, G. (1978) Estimating the dimantion of the model. Annals of Statistics 6:461–464.
Venables, W. N. & Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition. Springer, New York. ISBN 0-387-95457-0.
Wheaton, B., Muthen, B., Alwin, D. F., Summers, G. (1977) Assessing reliability and stability in panel models. Sociological Methodology 8:84–136.
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 | # The following model has been created with
# six observed endogenous variables,
# two unobserved endogenous variables and
# four unobserved exogenous variables.
S <- matrix(c(
1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0,
0.6321, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0,
0.5932, 0.5881, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0,
0.0965, 0.0987, 0.1564, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0,
0.1785, 0.1256, 0.1124, 0.4567, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0,
0.2135, 0.2003, 0.0762, 0.5589, 0.6097, 1.0000, 0.0000, 0.0000, 0.0000, 0,
0.3875, 0.4011, 0.3211, 0.0134, 0.0189, 0.0556, 1.0000, 0.0000, 0.0000, 0,
0.3569, 0.3989, 0.3301, 0.1323, 0.1036, 0.1132, 0.3215, 1.0000, 0.0000, 0,
0.1034, 0.1201, 0.1010, 0.2981, 0.3265, 0.2920, 0.1092, 0.0981, 1.0000, 0,
0.1324, 0.0622, 0.0123, 0.3056, 0.3525, 0.2661, 0.1234, 0.1207, 0.2221, 1
), ncol=10, byrow=TRUE)
rownames(S) <- c("Y1", "Y2", "Y3", "Y4", "Y5", "Y6",
"CSI1", "CSI2", "CSI3", "CSI4")
colnames(S) <- c("Y1", "Y2", "Y3", "Y4", "Y5", "Y6",
"CSI1", "CSI2", "CSI3", "CSI4")
ram.I <- matrix(c(
# heads to from param start
1, 1, 11, 1, NA, # lam1
1, 2, 11, 0, 0.750,
1, 3, 11, 2, NA, # lam2
1, 4, 12, 3, NA, # lam3
1, 5, 12, 4, NA, # lam4
1, 6, 12, 0, 0.800,
1, 11, 7, 5, NA, # gam1
1, 11, 8, 6, NA, # gam2
1, 12, 9, 7, NA, # gam3
1, 12, 10, 8, NA, # gam4
2, 1, 1, 9, NA, # theta1
2, 2, 2, 10, NA, # theta2
2, 3, 3, 11, NA, # theta3
2, 4, 4, 12, NA, # theta4
2, 5, 5, 13, NA, # theta5
2, 6, 6, 14, NA, # theta6
2, 11, 11, 15, NA, # psi1
2, 12, 12, 16, NA # psi2
), ncol=5, byrow=TRUE)
params.I <- c('lam1', 'lam2', 'lam3', 'lam4', 'gam1', 'gam2',
'gam3', 'gam4', 'theta1', 'theta2', 'theta3',
'theta4', 'theta5', 'theta6', 'psi1', 'psi2')
vars.I <- c('Y1', 'Y2', 'Y3', 'Y4', 'Y5', 'Y6', 'CSI1',
'CSI2', 'CSI3', 'CSI4', 'ETA1', 'ETA2')
sem.I <- sem(ram.I, S, 250, param.names=params.I,
var.names=vars.I, fixed.x=7:10)
summaryGOF(sem.I)
# Goodness-of-Fit indexes of structural equation models for 'sem' package
# ICOMP = -14.964
# Fml = 0.19582
# RNI = 0.97065
# IFI = 0.97133
# chisq.df = 1.6814
# CN = 231.91
# Gamma.hat = 0.98438
# BL86 = 0.89465
# W = 1.6814
# d = 0.079042
# Mc = 0.96125
# CAK = 0.27582
# CSK = 0.41668
# ECVI = 0.40466
|
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