How to set residual covariances in the SEM model?
763 views
Skip to first unread message
luquany...@gmail.com
May 5, 2016, 6:57:39 AM5/5/16
to lavaan
We I set the residual covariances, I find that different residual covariances setting will lead to different results.
I don not know how to set this part. If I delet this part, the results will also change.
library(lavaan)
x<-read.csv("C:/Users/Quanying LU/Desktop/5.csv")
> co2model<-'
+ # measurement model
+ co2=~y1
+ total=~y2+y3+y4+y5+y6
+ struct=~y7+y8+y9+y10
+ # regressions
+ co2~total+struct
+ total~struct
+ # residual covariances
+ y2~~y3+y4+y5+y6+y7+y8+y9+y10
+ y3 ~~ y4+y7+y9
+ y5 ~~ y4+y7+y8+y9
+ y6 ~~ y4+y7+y8+y9
+ y7~~y4
+ '
> fit <- sem(co2model, data = x,meanstructure = "default",
+ conditional.x = "default", fixed.x = "default",
+ orthogonal = FALSE, std.lv = FALSE,
+ parameterization = "default", std.ov = FALSE,
+ missing = "default", ordered = NULL,
+ sample.cov = NULL, sample.cov.rescale = "default",
+ sample.mean = NULL, sample.nobs = NULL,
+ ridge = 1e-05, group = NULL,
+ group.label = NULL, group.equal = "", group.partial = "",
+ group.w.free = FALSE, cluster = NULL, constraints = '',
+ estimator = "default", likelihood = "default", link = "default",
+ information = "default", se = "default", test = "default",
+ bootstrap = 1000L, mimic = "default", representation = "default",
+ do.fit = TRUE, control = list(), WLS.V = NULL, NACOV = NULL,
+ zero.add = "default", zero.keep.margins = "default",zero.cell.warn = TRUE,
+ start = "default", verbose = FALSE, warn = TRUE, debug = FALSE)
Warning messages:
1: In lav_object_post_check(lavobject) :
lavaan WARNING: some estimated variances are negative
2: In lav_object_post_check(lavobject) :
lavaan WARNING: covariance matrix of latent variables is not positive definite; use inspect(fit,"cov.lv") to investigate.
3: In lav_object_post_check(lavobject) :
lavaan WARNING: observed variable error term matrix (theta) is not positive definite; use inspect(fit,"theta") to investigate.
> summary(fit, standardized = TRUE)
lavaan (0.5-20) converged normally after 444 iterations
Number of observations 27
Estimator ML
Minimum Function Test Statistic 71.870
Degrees of freedom 13
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
co2 =~
y1 1.000 0.863 1.000
total =~
y2 1.000 0.744 0.974
y3 0.093 0.003 28.033 0.000 0.069 0.966
y4 1.544 0.040 38.915 0.000 1.149 0.974
y5 1.064 0.085 12.521 0.000 0.792 0.914
y6 0.655 0.041 16.166 0.000 0.487 0.952
struct =~
y7 1.000 0.244 0.998
y8 0.195 0.059 3.327 0.001 0.047 0.521
y9 2.784 0.079 35.086 0.000 0.679 0.991
y10 -1.060 0.058 -18.176 0.000 -0.259 -0.962
Regressions:
Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
co2 ~
total 0.630 0.146 4.319 0.000 0.544 0.544
struct 1.571 0.449 3.497 0.000 0.444 0.444
total ~
struct 3.118 0.144 21.684 0.000 1.022 1.022
Covariances:
Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
y2 ~~
y3 0.002 0.001 3.680 0.000 0.002 0.729
y4 0.038 0.009 4.221 0.000 0.038 0.832
y5 0.021 0.006 3.798 0.000 0.021 0.352
y6 0.009 0.002 3.519 0.000 0.009 0.318
y7 -0.004 0.001 -4.050 0.000 -0.004 -1.692
y8 -0.001 0.001 -1.265 0.206 -0.001 -0.072
y9 -0.004 0.001 -2.996 0.003 -0.004 -0.255
y10 -0.005 0.001 -3.929 0.000 -0.005 -0.366
y3 ~~
y4 0.004 0.001 3.921 0.000 0.004 0.855
y7 -0.000 0.000 -4.410 0.000 -0.000 -1.620
y9 0.000 0.000 2.653 0.008 0.000 0.282
y4 ~~
y5 0.028 0.009 3.162 0.002 0.028 0.299
y5 ~~
y7 -0.002 0.002 -1.547 0.122 -0.002 -0.485
y8 0.010 0.003 3.037 0.002 0.010 0.384
y9 -0.016 0.004 -3.668 0.000 -0.016 -0.503
y4 ~~
y6 0.007 0.003 2.539 0.011 0.007 0.172
y6 ~~
y7 -0.003 0.001 -3.317 0.001 -0.003 -1.159
y8 -0.009 0.002 -3.677 0.000 -0.009 -0.756
y9 -0.008 0.002 -3.574 0.000 -0.008 -0.583
y4 ~~
y7 -0.006 0.002 -4.079 0.000 -0.006 -1.731
Variances:
Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
y1 0.000 0.000 0.000
y2 0.030 0.007 4.443 0.000 0.030 0.051
y3 0.000 0.000 3.899 0.000 0.000 0.066
y4 0.070 0.015 4.562 0.000 0.070 0.051
y5 0.123 0.030 4.082 0.000 0.123 0.164
y6 0.024 0.007 3.660 0.000 0.024 0.093
y7 0.000 0.000 1.878 0.060 0.000 0.003
y8 0.006 0.001 4.063 0.000 0.006 0.729
y9 0.009 0.002 4.547 0.000 0.009 0.019
y10 0.005 0.001 4.521 0.000 0.005 0.074
co2 0.011 0.004 2.870 0.004 0.014 0.014
total -0.024 0.007 -3.360 0.001 -0.044 -0.044
struct 0.059 0.016 3.662 0.000 1.000 1.000
> library(lavaan)
> x<-read.csv("C:/Users/Quanying LU/Desktop/5.csv")
> co2model<-'
+ # measurement model
+ co2=~y1
+ total=~y2+y3+y4+y5+y6
+ struct=~y7+y8+y9+y10
+ # regressions
+ co2~total+struct
+ total~struct
+ # residual covariances
+ y2~~y3+y4+y5+y6+y7+y8+y9+y10
+ y3 ~~ y4+y7
+ y5 ~~ y7+y8+y9
+ y6~~y7+y8+y9
+ y9~~y4'
> fit <- sem(co2model, data = x,meanstructure = "default",
+ conditional.x = "default", fixed.x = "default",
+ orthogonal = FALSE, std.lv = FALSE,
+ parameterization = "default", std.ov = FALSE,
+ missing = "default", ordered = NULL,
+ sample.cov = NULL, sample.cov.rescale = "default",
+ sample.mean = NULL, sample.nobs = NULL,
+ ridge = 1e-05,group = NULL,
+ group.label = NULL, group.equal = "", group.partial = "",
+ group.w.free = FALSE, cluster = NULL, constraints = '',
+ estimator = "default", likelihood = "default", link = "default",
+ information = "default", se = "default", test = "default",
+ bootstrap = 1000L, mimic = "default", representation = "default",
+ do.fit = TRUE, control = list(), WLS.V = NULL, NACOV = NULL,
+ zero.add = "default", zero.keep.margins = "default",zero.cell.warn = TRUE,
+ start = "default", verbose = FALSE, warn = TRUE, debug = FALSE)
Warning messages:
1: In lav_object_post_check(lavobject) :
lavaan WARNING: some estimated variances are negative
2: In lav_object_post_check(lavobject) :
lavaan WARNING: covariance matrix of latent variables is not positive definite; use inspect(fit,"cov.lv") to investigate.
3: In lav_object_post_check(lavobject) :
lavaan WARNING: observed variable error term matrix (theta) is not positive definite; use inspect(fit,"theta") to investigate.
> summary(fit, standardized = TRUE)
lavaan (0.5-20) converged normally after 481 iterations
Number of observations 27
Estimator ML
Minimum Function Test Statistic 121.532
Degrees of freedom 16
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
co2 =~
y1 1.000 0.863 1.000
total =~
y2 1.000 0.746 0.981
y3 0.094 0.003 31.389 0.000 0.070 0.978
y4 1.524 0.061 24.967 0.000 1.136 0.968
y5 1.054 0.089 11.877 0.000 0.786 0.909
y6 0.654 0.038 17.081 0.000 0.487 0.957
struct =~
y7 1.000 0.242 0.996
y8 0.196 0.058 3.400 0.001 0.047 0.538
y9 2.822 0.074 38.310 0.000 0.682 0.995
y10 -1.071 0.060 -17.816 0.000 -0.259 -0.963
Regressions:
Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
co2 ~
total 0.549 0.145 3.797 0.000 0.475 0.475
struct 1.831 0.448 4.085 0.000 0.513 0.513
total ~
struct 3.137 0.132 23.853 0.000 1.017 1.017
Covariances:
Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
y2 ~~
y3 0.002 0.000 3.291 0.001 0.002 0.678
y4 0.027 0.009 3.041 0.002 0.027 0.612
y5 0.016 0.005 3.339 0.001 0.016 0.302
y6 0.007 0.002 3.211 0.001 0.007 0.302
y7 -0.003 0.001 -4.815 0.000 -0.003 -0.932
y8 -0.001 0.001 -1.036 0.300 -0.001 -0.071
y9 -0.004 0.001 -3.359 0.001 -0.004 -0.434
y10 -0.004 0.001 -3.778 0.000 -0.004 -0.393
y3 ~~
y4 0.002 0.001 2.417 0.016 0.002 0.513
y7 -0.000 0.000 -4.909 0.000 -0.000 -1.266
y5 ~~
y7 -0.004 0.001 -3.114 0.002 -0.004 -0.558
y8 0.011 0.004 2.865 0.004 0.011 0.422
y9 -0.019 0.005 -4.097 0.000 -0.019 -0.750
y6 ~~
y7 -0.003 0.001 -4.324 0.000 -0.003 -0.928
y8 -0.008 0.002 -3.446 0.001 -0.008 -0.732
y9 -0.009 0.002 -3.770 0.000 -0.009 -0.869
y4 ~~
y9 0.005 0.003 1.629 0.103 0.005 0.235
Variances:
Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
y1 0.000 0.000 0.000
y2 0.022 0.005 4.058 0.000 0.022 0.038
y3 0.000 0.000 4.068 0.000 0.000 0.044
y4 0.088 0.022 3.943 0.000 0.088 0.064
y5 0.130 0.033 3.897 0.000 0.130 0.174
y6 0.022 0.006 3.558 0.000 0.022 0.084
y7 0.000 0.000 2.540 0.011 0.000 0.008
y8 0.006 0.001 4.055 0.000 0.006 0.711
y9 0.005 0.001 4.929 0.000 0.005 0.010
y10 0.005 0.001 4.557 0.000 0.005 0.073
co2 0.013 0.003 4.023 0.000 0.017 0.017
total -0.019 0.006 -3.048 0.002 -0.034 -0.034
struct 0.058 0.016 3.645 0.000 1.000 1.000
library(lavaan)
> x<-read.csv("C:/Users/Quanying LU/Desktop/5.csv")
> co2model<-'
+ # measurement model
+ co2=~y1
+ total=~y2+y3+y4+y5+y6
+ struct=~y7+y8+y9+y10
+ # regressions
+ co2~total+struct
+ total~struct
+ '
> fit <- sem(co2model, data = x,meanstructure = "default",
+ conditional.x = "default", fixed.x = "default",
+ orthogonal = FALSE, std.lv = FALSE,
+ parameterization = "default", std.ov = FALSE,
+ missing = "default", ordered = NULL,
+ sample.cov = NULL, sample.cov.rescale = "default",
+ sample.mean = NULL, sample.nobs = NULL,
+ ridge = 1e-05,group = NULL,
+ group.label = NULL, group.equal = "", group.partial = "",
+ group.w.free = FALSE, cluster = NULL, constraints = '',
+ estimator = "default", likelihood = "default", link = "default",
+ information = "default", se = "default", test = "default",
+ bootstrap = 1000L, mimic = "default", representation = "default",
+ do.fit = TRUE, control = list(), WLS.V = NULL, NACOV = NULL,
+ zero.add = "default", zero.keep.margins = "default",zero.cell.warn = TRUE,
+ start = "default", verbose = FALSE, warn = TRUE, debug = FALSE)
Warning messages:
1: In lav_object_post_check(lavobject) :
lavaan WARNING: some estimated variances are negative
2: In lav_object_post_check(lavobject) :
lavaan WARNING: covariance matrix of latent variables is not positive definite; use inspect(fit,"cov.lv") to investigate.
3: In lav_object_post_check(lavobject) :
lavaan WARNING: observed variable error term matrix (theta) is not positive definite; use inspect(fit,"theta") to investigate.
> summary(fit, standardized = TRUE)
lavaan (0.5-20) converged normally after 159 iterations
Number of observations 27
Estimator ML
Minimum Function Test Statistic 232.481
Degrees of freedom 33
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
co2 =~
y1 1.000 0.863 1.000
total =~
y2 1.000 0.757 1.000
y3 0.092 0.004 21.444 0.000 0.069 0.972
y4 1.532 0.048 31.653 0.000 1.159 0.987
y5 1.048 0.081 12.980 0.000 0.793 0.928
y6 0.657 0.043 15.396 0.000 0.497 0.947
struct =~
y7 1.000 0.243 0.996
y8 0.160 0.054 2.958 0.003 0.039 0.494
y9 2.786 0.102 27.187 0.000 0.677 0.986
y10 -1.085 0.045 -24.145 0.000 -0.264 -0.982
Regressions:
Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
co2 ~
total -0.618 0.398 -1.551 0.121 -0.542 -0.542
struct 5.468 1.244 4.395 0.000 1.540 1.540
total ~
struct 3.098 0.080 38.568 0.000 0.995 0.995
Variances:
Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
y1 0.000 0.000 0.000
y2 -0.000 0.001 -0.322 0.748 -0.000 -0.001
y3 0.000 0.000 3.669 0.000 0.000 0.056
y4 0.037 0.010 3.545 0.000 0.037 0.027
y5 0.101 0.027 3.685 0.000 0.101 0.139
y6 0.028 0.008 3.686 0.000 0.028 0.103
y7 0.001 0.000 3.395 0.001 0.001 0.008
y8 0.005 0.001 3.682 0.000 0.005 0.756
y9 0.013 0.003 3.878 0.000 0.013 0.027
y10 0.003 0.001 3.904 0.000 0.003 0.037
co2 -0.004 0.003 -1.424 0.154 -0.005 -0.005
total 0.006 0.003 2.034 0.042 0.010 0.010
struct 0.059 0.016 3.643 0.000 1.000 1.000
Terrence Jorgensen
May 6, 2016, 7:01:29 AM5/6/16
to lavaan
Just like in your previous post, you are already specifying residual covariances correctly. It looks like your question was already answered on the blavaan group: https://groups.google.com/d/msg/blavaan/YBN43AcKO7k/hzvW7hMEBgAJ
luquany...@gmail.com
May 7, 2016, 2:59:07 AM5/7/16
to lavaan
I have a puzzle. If we do not have a tiny sample size, add "co2~~0.01*co2", whether the results will be affected?
Whether we can change "total~~0.01*total" or "struct~~0.01*struct"? What is the foundation? Exogenous variable? Endogenous Variable?
Please forgive me for interrupting!
Thank you very much!
在 2016年5月6日星期五 UTC+8下午7:01:29，Terrence Jorgensen写道：
Mauricio Garnier-Villarreal
May 7, 2016, 12:59:21 PM5/7/16
to lavaan
this line co2~~0.01*co2 fixes the variance of co2 to the value 0.01, so it will not be estimated
luquany...@gmail.com
May 8, 2016, 10:21:09 PM5/8/16
to lavaan
If I delete it, it will also not be estimated.
在 2016年5月8日星期日 UTC+8上午12:59:21，Mauricio Garnier-Villarreal写道：
在 2016年5月8日星期日 UTC+8上午12:59:21，Mauricio Garnier-Villarreal写道：
Terrence Jorgensen
May 9, 2016, 6:24:57 AM5/9/16
to lavaan
If I delete it, it will also not be estimated.
This is a free estimate: co2 ~~ co2 (or) co2 ~~ NA*co2
This is a free estimate, with a starting value: co2 ~~ 0.01?co2
This is a fixed estimated: co2 ~~ 0.01*co2
Deleting the line altogether from your syntax implies you want it fixed to zero, so it is equivalent to including this line of syntax:
co2 ~~ 0*co2
Terrence D. Jorgensen
Postdoctoral Researcher, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
UvA web page: http://www.uva.nl/profile/t.d.jorgensen
luquany...@gmail.com
May 9, 2016, 10:39:08 AM5/9/16
to lavaan
Dear Terrence D. Jorgensen:
Thank you for your help!
I tried to correct it like you said. I add co2 ~~ co2 (or) co2 ~~ NA*co2, the error could not be corrected. I do not know why.
Warning messages:
1: In lav_object_post_check(lavobject) :
lavaan WARNING: some estimated variances are negative
2: In lav_object_post_check(lavobject) :
lavaan WARNING: covariance matrix of latent variables is not positive definite; use inspect(fit,"cov.lv") to investigate.
3: In lav_object_post_check(lavobject) :
lavaan WARNING: observed variable error term matrix (theta) is not positive definite; use inspect(fit,"theta") to investigate.
在 2016年5月9日星期一 UTC+8下午6:24:57，Terrence Jorgensen写道：
Reply all
Reply to author
Forward
0 new messages