Heywood case: lavaan warning message: some estimated variances are negative

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Diego

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Aug 31, 2018, 5:40:26 AM8/31/18

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Hi lavaan group,

I have been trying different model specification for my sem model but always ended up with a Heywood case (probably induced by the small sample size and partially by the model misspecification).

> fit <- cfa(model, data=x_dat, estimator="MLM", std.lv=TRUE, test = "bootstrap", likelihood = "wishart") #WLSMV
Warning message:
In lav_object_post_check(object) :
  lavaan WARNING: some estimated ov variances are negative

I have read the forum looking for similar cases and try to improve the model, but it did not help. I based my model on a previous PCA and EFA results.

model <- '

# measurement model

factor_1 =~ Organic_N + Organic_P2O5 + Organic_K2O + Animal + Human

factor_2 =~ Inorganic_N + Inorganic_P2O5 + Inorganic_K2O + Machinery + CED + HT + FAET + MAET + Fungicide + Insecticide

factor_3 =~ GWP + AP + EP

# regressions/structural

factor_1 ~ factor_3

factor_2 ~ factor_3

# residual correlations

HT ~~ FAET

HT ~~ MAET

FAET ~~ MAET

CED ~~ Machinery

Inorganic_P2O5 ~~ MAET

AP ~~ EP

I tried to set the first loading of factor_1 equal to 1 (1*Organic_N) but it did not work.

> inspect(fit,what="std")$lambda #loadings

fctr_1 fctr_2 fctr_3

Organic_N 1.019 0.000 0.000

Organic_P2O5 0.877 0.000 0.000

Organic_K2O 0.833 0.000 0.000

Animal 0.509 0.000 0.000

Human 0.684 0.000 0.000

Inorganic_N 0.000 0.881 0.000

Inorganic_P2O5 0.000 0.863 0.000

Inorganic_K2O 0.000 0.904 0.000

Machinery 0.000 0.465 0.000

CED 0.000 0.892 0.000

HT 0.000 0.828 0.000

FAET 0.000 0.755 0.000

MAET 0.000 0.623 0.000

Fungicide 0.000 0.502 0.000

Insecticide 0.000 0.298 0.000

GWP 0.000 0.000 0.982

AP 0.000 0.000 0.856

EP 0.000 0.000 0.710

This is the fit of my model:

> summary(fit, standardized=TRUE, fit.measures=TRUE, rsquare=TRUE, ci=TRUE)

lavaan 0.6-2 ended normally after 76 iterations

  Optimization method                           NLMINB

  Number of free parameters                         44

  Number of observations                            58

  Estimator                                         ML      Robust

  Model Fit Test Statistic                     436.301     293.327

  Degrees of freedom                               127         127

  P-value (Chi-square)                           0.000       0.000

  Scaling correction factor                                  1.487

    for the Satorra-Bentler correction

Model test baseline model:

  Minimum Function Test Statistic             1591.910     820.132

  Degrees of freedom                               153         153

  P-value                                        0.000       0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.785       0.751

  Tucker-Lewis Index (TLI)                       0.741       0.700

  Robust Comparative Fit Index (CFI)                         0.809

  Robust Tucker-Lewis Index (TLI)                            0.770

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)               -893.430    -893.430

  Loglikelihood unrestricted model (H1)       -671.453    -671.453

  Number of free parameters                         44          44

  Akaike (AIC)                                1874.861    1874.861

  Bayesian (BIC)                              1965.520    1965.520

  Sample-size adjusted Bayesian (BIC)         1827.177    1827.177

Root Mean Square Error of Approximation:

  RMSEA                                          0.207       0.152

  90 Percent Confidence Interval          0.186  0.228       0.133  0.170

  P-value RMSEA <= 0.05                          0.000       0.000

  Robust RMSEA                                               0.185

  90 Percent Confidence Interval                             0.157  0.213

Standardized Root Mean Square Residual:

  SRMR                                           0.186       0.186

Parameter Estimates:

  Information                                 Expected

  Information saturated (h1) model          Structured

  Standard Errors                           Robust.sem

Latent Variables:

                   Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all

  factor_1 =~

    Organic_N         1.000                               1.000    1.000    1.173    1.019

    Organic_P2O5      0.837    0.099    8.455    0.000    0.643    1.031    0.982    0.877

    Organic_K2O       0.786    0.100    7.825    0.000    0.589    0.983    0.922    0.833

    Animal            0.449    0.179    2.513    0.012    0.099    0.799    0.527    0.509

    Human             0.623    0.093    6.684    0.000    0.440    0.805    0.730    0.684

  factor_2 =~

    Inorganic_N       0.833    0.106    7.870    0.000    0.625    1.040    0.966    0.881

    Inorganic_P2O5    0.812    0.079   10.251    0.000    0.657    0.968    0.942    0.863

    Inorganic_K2O     0.859    0.089    9.661    0.000    0.685    1.034    0.996    0.904

    Machinery         0.410    0.132    3.098    0.002    0.151    0.670    0.476    0.465

    CED               0.846    0.093    9.071    0.000    0.663    1.028    0.981    0.892

    HT                0.773    0.075   10.304    0.000    0.626    0.920    0.897    0.828

    FAET              0.695    0.094    7.403    0.000    0.511    0.879    0.806    0.755

    MAET              0.560    0.112    4.983    0.000    0.340    0.780    0.649    0.623

    Fungicide         0.445    0.167    2.669    0.008    0.118    0.772    0.516    0.502

    Insecticide       0.259    0.115    2.252    0.024    0.034    0.485    0.301    0.298

  factor_3 =~

    GWP               0.982    0.083   11.822    0.000    0.819    1.144    0.982    0.982

    AP                0.856    0.106    8.106    0.000    0.649    1.063    0.856    0.856

    EP                0.710    0.134    5.314    0.000    0.448    0.972    0.710    0.710

Regressions:

                   Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all

  factor_1 ~

    factor_3          0.613    0.188    3.260    0.001    0.244    0.981    0.523    0.523

  factor_2 ~

    factor_3          0.587    0.184    3.189    0.001    0.226    0.948    0.506    0.506

Covariances:

                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all

 .HT ~~

   .FAET               0.413    0.097    4.240    0.000    0.222    0.604    0.413    0.970

   .MAET               0.460    0.105    4.370    0.000    0.254    0.667    0.460    0.928

 .FAET ~~

   .MAET               0.544    0.129    4.222    0.000    0.292    0.797    0.544    0.953

 .Machinery ~~

   .CED                0.323    0.169    1.904    0.057   -0.009    0.655    0.323    0.717

 .Inorganic_P2O5 ~~

   .MAET               0.142    0.046    3.125    0.002    0.053    0.232    0.142    0.317

 .AP ~~

   .EP                 0.208    0.079    2.638    0.008    0.053    0.362    0.208    0.570

 .factor_1 ~~

   .factor_2          -0.897    0.043  -20.869    0.000   -0.981   -0.813   -0.897   -0.897

Variances:

                   Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all

   .Organic_N        -0.052    0.032   -1.595    0.111   -0.115    0.012   -0.052   -0.039

   .Organic_P2O5      0.289    0.074    3.910    0.000    0.144    0.434    0.289    0.230

   .Organic_K2O       0.374    0.118    3.167    0.002    0.142    0.605    0.374    0.305

   .Animal            0.795    0.280    2.840    0.005    0.246    1.344    0.795    0.741

   .Human             0.607    0.160    3.795    0.000    0.293    0.920    0.607    0.532

   .Inorganic_N       0.269    0.111    2.430    0.015    0.052    0.486    0.269    0.224

   .Inorganic_P2O5    0.305    0.089    3.408    0.001    0.129    0.480    0.305    0.256

   .Inorganic_K2O     0.222    0.070    3.155    0.002    0.084    0.359    0.222    0.183

   .Machinery         0.822    0.417    1.973    0.048    0.006    1.639    0.822    0.784

   .CED               0.246    0.078    3.149    0.002    0.093    0.399    0.246    0.204

   .HT                0.370    0.085    4.331    0.000    0.203    0.537    0.370    0.315

   .FAET              0.491    0.120    4.091    0.000    0.256    0.726    0.491    0.430

   .MAET              0.664    0.143    4.646    0.000    0.384    0.945    0.664    0.612

   .Fungicide         0.791    0.279    2.836    0.005    0.244    1.338    0.791    0.748

   .Insecticide       0.929    0.697    1.334    0.182   -0.436    2.294    0.929    0.911

   .GWP               0.037    0.028    1.306    0.192   -0.018    0.091    0.037    0.037

   .AP                0.268    0.069    3.887    0.000    0.133    0.402    0.268    0.268

   .EP                0.496    0.142    3.500    0.000    0.218    0.773    0.496    0.496

   .factor_1          1.000                               1.000    1.000    0.727    0.727

   .factor_2          1.000                               1.000    1.000    0.744    0.744

    factor_3          1.000                               1.000    1.000    1.000    1.000

R-Square:

                   Estimate

    Organic_N            NA

    Organic_P2O5      0.770

    Organic_K2O       0.695

    Animal            0.259

    Human             0.468

    Inorganic_N       0.776

    Inorganic_P2O5    0.744

    Inorganic_K2O     0.817

    Machinery         0.216

    CED               0.796

    HT                0.685

    FAET              0.570

    MAET              0.388

    Fungicide         0.252

    Insecticide       0.089

    GWP               0.963

    AP                0.732

    EP                0.504

    factor_1          0.273

    factor_2          0.256

Do you have any plausible solution or advice to deal with this error?

Thanks in advance,

Diego

Edward Rigdon

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Aug 31, 2018, 9:27:34 AM8/31/18

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You have 58 observations estimating 44 free parameters, so there is no reaon to expect good results. However, in these results you request standardized output. That is why your attempted constraint of a loading to 1 does not appear. Your constraints apply to the original, unstandardized parameter estimates. It is possible to impose them at the standardized level, but that is unrelated to the warning message. To force that residual variance to be nonnegative, you will need to constrain that parameter directly, as in:

varA ~~ 0 * varA

varA ~~ steve * varA

steve > 0

s...@gmail.com> wrote:

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Fabrício Fialho

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Mar 3, 2019, 7:14:00 PM3/3/19

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Hi all,

I wonder if the syntax to constrain residuals in lavaan 0.6x changed in comparison to previous versions. For some reason, I cannot apply constrain to residuals. For instance, in one model, I have experienced Heywood cases and I tried to constrain the residual to be >= 0.

If I try to constrain it to == 0 (I use Ed's 'steve' fun example here):

q13.i4 ~~ steve*q13.i4
steve == 0

residual variance remains negative

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
(...)
   .q13.i4  (stev)   -0.132                              -0.132   -0.132
(...)

If I try to constrain steve to be > 0,

q13.i4 ~~ steve*q13.i4
steve > 0

then the model does not converge.

What could be causing this? Not sure this might make any sense, but I wonder if the issue is in OPTIMIZER internal to lavaan. I notice if I set "optim.method" to be "nlminb", "BFGS" or "L-BFGS-B", lavaan works. However, if I set "optim.method" to be "nlminb.constr" I receive the following error message:

Error in lav_model_estimate(lavmodel = lavmodel, lavpartable = lavpartable,  : 
  OPTIMIZER %in% c("NLMINB0", "NLMINB1", "NLMINB2", "NLMINB", "BFGS",  .... is not TRUE

Thanks!

Terrence Jorgensen

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Mar 6, 2019, 2:51:07 PM3/6/19

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It works as expected in the latest development version (0.6-4.1349)

HS.model <- ' visual  =~ x1 + x2 + x3
              textual =~ x4 + x5 + x6
              speed   =~ x7 + x8 + x9 
visual ~~ steve*speed '
# returns 0 for this correlation
summary(cfa(HS.model, data=HolzingerSwineford1939, constraints = 'steve == 0'))
# cannot find a solution with a negative covariance
summary(cfa(HS.model, data=HolzingerSwineford1939, constraints = 'steve < 0'))

If I try to constrain steve to be > 0, the model does not converge. What could be causing this?

There must not be a good solution that includes positive values of that parameter. Constraining variances to be positive has negative consequences anyway.

Savalei, V., & Kolenikov, S. (2008). Constrained versus unconstrained estimation in structural equation modeling. Psychological Methods, 13(2), 150.

Better to leave it unconstrained, and simply test the null hypothesis that the value is truly nonnegative in the population by checking that the CI includes positive values.

https://doi.org/10.1177/0049124112442138

summary(fit, ci = TRUE)

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

Stas Kolenikov

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Mar 6, 2019, 3:59:33 PM3/6/19

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Thanks for advertising our work, Terrence :)

Diego, what is the goal of your SEM exercise? None of the research that uses SEM is going to discuss and interpret EVERY parameter in the model. Most of the time, you just want the factor regressions, or something like that. If that is the case, the Heywood case in one of the measurement equations is weird and annoying, but does not necessarily negate the whole model. You can throw in more error correlations and see if the principal parameters of your interest change. And if your interest is indeed in the factor regressions, you can at least try Bollen's model-implied instrumental variables.

Constraining variances to be non-negative is one thing. Constraining them to be strictly positive is another: if the unconstrained estimated variance is negative, then the optimization algorithm will be just trying to make the number as small as possible, but may never be able to declare convergence because the numbers keep changing. With a non-negative constraint, you at least give the program a chance to bookend at zero. Generally, optimization with constraints of the type > or >= is far more complicated than with equality constraints, and details of what exactly you are asking the software to do may matter a lot.

Finally, as Ed pointed out a few emails earlier, a model with 127 estimated parameters based on 58 observations is... uhm... unconvincing. And Satorra-Benter corrections that need stable fourth-order moment estimates are less convincing still -- they really require sample sizes in a few thousands to produce anything meaningful. Again, MIIV could be a better deal for you given the tiny sample size.

-- Stas Kolenikov, PhD, PStat (ASA, SSC) @StatStas
-- Principal Scientist, Abt Associates @AbtDataScience
-- Opinions stated in this email are mine only, and do not reflect the position of my employer
-- http://stas.kolenikov.name

Burt Hatch

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Nov 17, 2019, 8:59:02 PM11/17/19

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Hi all,

I have an issue related to this post.

I am estimating a bifactor model with ordinal data for the purpose of determining proportion of variance attributable to a general factor vs specific factors.

I am estimating the model using 100 multiply imputed data sets with a sample of 452 using the semTools cfa.mi function. The output of the model is pasted below. One Item (.CSH_S4a) has a negative estimated variance. My question is, how do I calculate the CI for this variance using any of the methods in "Savalei, V., & Kolenikov, S. (2008). Constrained versus unconstrained estimation in structural equation modeling. Psychological Methods, 13(2), 150." ?

Sorry if I am missing something obvious here and thank you in advance for your time.

Burt

Parameter Estimates:

Information Expected

Information saturated (h1) model Unstructured

Standard errors Robust.sem

Latent Variables:

Estimate Std.Err t-value df P(>|t|) ci.lower ci.upper

A =~

CSH_B3a 0.155 0.074 2.098 Inf 0.036 0.010 0.299

CSH_S4a 0.793 0.103 7.663 Inf 0.000 0.590 0.996

CSH_S5a 0.430 0.080 5.406 Inf 0.000 0.274 0.586

CSH_S2a 0.443 0.073 6.103 Inf 0.000 0.301 0.585

CSH_B11a 0.069 0.081 0.852 Inf 0.394 -0.090 0.229

CSH_B2a 0.071 0.087 0.815 Inf 0.415 -0.100 0.243

B =~

CSH_B8a 0.737 0.037 20.089 Inf 0.000 0.665 0.808

CSH_B13a 0.573 0.054 10.691 Inf 0.000 0.468 0.679

CSH_B4a 0.842 0.036 23.644 Inf 0.000 0.772 0.912

CSH_B5a 0.730 0.041 17.997 Inf 0.000 0.650 0.809

CSH_S10a 0.272 0.063 4.316 Inf 0.000 0.149 0.396

C =~

CSH_S19a 0.461 0.083 5.558 Inf 0.000 0.299 0.624

CSH_W2a 0.557 0.075 7.468 Inf 0.000 0.411 0.703

CSH_S7a 0.377 0.089 4.247 Inf 0.000 0.203 0.551

CSH_S8a 0.213 0.073 2.924 Inf 0.003 0.070 0.355

CSH_W1a 0.506 0.078 6.515 Inf 0.000 0.354 0.658

D =~

CSH_M7a 0.646 0.049 13.058 Inf 0.000 0.549 0.743

CSH_M6a 0.791 0.035 22.329 Inf 0.000 0.721 0.860

CSH_M4a 0.422 0.052 8.155 Inf 0.000 0.321 0.524

CSH_D3a -0.019 0.060 -0.320 Inf 0.749 -0.137 0.098

CSH_M5a 0.861 0.030 28.740 Inf 0.000 0.802 0.919

CSH_M2a 0.909 0.031 29.240 Inf 0.000 0.848 0.970

G =~

CSH_B3a 0.536 0.050 10.613 Inf 0.000 0.437 0.635

CSH_S4a 0.711 0.053 13.491 Inf 0.000 0.608 0.814

CSH_S5a 0.487 0.065 7.438 Inf 0.000 0.359 0.615

CSH_S2a 0.710 0.043 16.345 Inf 0.000 0.625 0.796

CSH_B11a 0.673 0.044 15.246 Inf 0.000 0.587 0.760

CSH_B2a 0.645 0.054 11.932 Inf 0.000 0.539 0.751

CSH_B8a 0.486 0.052 9.266 Inf 0.000 0.383 0.589

CSH_B13a 0.514 0.055 9.325 Inf 0.000 0.406 0.622

CSH_B4a 0.526 0.052 10.144 Inf 0.000 0.424 0.627

CSH_B5a 0.447 0.057 7.893 Inf 0.000 0.336 0.558

CSH_S10a 0.449 0.057 7.898 Inf 0.000 0.337 0.560

CSH_S19a 0.403 0.067 6.024 Inf 0.000 0.272 0.534

CSH_W2a 0.607 0.054 11.214 Inf 0.000 0.501 0.713

CSH_S7a 0.313 0.070 4.466 Inf 0.000 0.176 0.451

CSH_S8a 0.569 0.048 11.885 Inf 0.000 0.475 0.662

CSH_W1a 0.539 0.050 10.887 Inf 0.000 0.442 0.636

CSH_M7a 0.377 0.064 5.861 Inf 0.000 0.251 0.503

CSH_M6a 0.316 0.066 4.771 Inf 0.000 0.186 0.445

CSH_M4a 0.437 0.057 7.700 Inf 0.000 0.325 0.548

CSH_D3a 0.380 0.059 6.428 4801.702 0.000 0.264 0.496

CSH_M5a 0.098 0.061 1.594 Inf 0.111 -0.022 0.218

CSH_M2a 0.089 0.069 1.276 Inf 0.202 -0.047 0.224

Covariances:

Estimate Std.Err t-value df P(>|t|) ci.lower ci.upper

A ~~

G 0.000 0.000 0.000

B ~~

G 0.000 0.000 0.000

C ~~

G 0.000 0.000 0.000

D ~~

G 0.000 0.000 0.000

A ~~

B 0.000 0.000 0.000

C 0.000 0.000 0.000

D 0.000 0.000 0.000

B ~~

C 0.000 0.000 0.000

D 0.000 0.000 0.000

C ~~

D 0.000 0.000 0.000

Intercepts:

Estimate Std.Err t-value df P(>|t|) ci.lower ci.upper

.CSH_B3a 0.000 0.000 0.000

.CSH_S4a 0.000 0.000 0.000

.CSH_S5a 0.000 0.000 0.000

.CSH_S2a 0.000 0.000 0.000

.CSH_B11a 0.000 0.000 0.000

.CSH_B2a 0.000 0.000 0.000

.CSH_B8a 0.000 0.000 0.000

.CSH_B13a 0.000 0.000 0.000

.CSH_B4a 0.000 0.000 0.000

.CSH_B5a 0.000 0.000 0.000

.CSH_S10a 0.000 0.000 0.000

.CSH_S19a 0.000 0.000 0.000

.CSH_W2a 0.000 0.000 0.000

.CSH_S7a 0.000 0.000 0.000

.CSH_S8a 0.000 0.000 0.000

.CSH_W1a 0.000 0.000 0.000

.CSH_M7a 0.000 0.000 0.000

.CSH_M6a 0.000 0.000 0.000

.CSH_M4a 0.000 0.000 0.000

.CSH_D3a 0.000 0.000 0.000

.CSH_M5a 0.000 0.000 0.000

.CSH_M2a 0.000 0.000 0.000

A 0.000 0.000 0.000

B 0.000 0.000 0.000

C 0.000 0.000 0.000

D 0.000 0.000 0.000

G 0.000 0.000 0.000

Thresholds:

Estimate Std.Err t-value df P(>|t|) ci.lower ci.upper

CSH_B3a|t1 0.058 0.057 1.021 Inf 0.307 -0.053 0.169

CSH_B3a|t2 0.999 0.068 14.645 Inf 0.000 0.865 1.132

CSH_S4a|t1 0.476 0.059 8.074 Inf 0.000 0.361 0.592

CSH_S4a|t2 1.250 0.076 16.457 Inf 0.000 1.101 1.399

CSH_S5a|t1 0.845 0.065 13.086 Inf 0.000 0.718 0.971

CSH_S5a|t2 1.637 0.095 17.255 Inf 0.000 1.451 1.823

CSH_S2a|t1 0.231 0.057 4.050 Inf 0.000 0.119 0.343

CSH_S2a|t2 1.217 0.075 16.280 Inf 0.000 1.071 1.364

CSH_B11a|t1 0.058 0.057 1.019 Inf 0.308 -0.053 0.169

CSH_B11a|t2 1.050 0.070 15.088 Inf 0.000 0.914 1.187

CSH_B2a|t1 0.569 0.060 9.486 Inf 0.000 0.452 0.687

CSH_B2a|t2 1.514 0.088 17.255 Inf 0.000 1.342 1.686

CSH_B8a|t1 0.115 0.057 2.030 Inf 0.042 0.004 0.226

CSH_B8a|t2 0.510 0.059 8.600 Inf 0.000 0.394 0.627

CSH_B13a|t1 0.530 0.060 8.882 Inf 0.000 0.413 0.647

CSH_B13a|t2 0.957 0.067 14.252 Inf 0.000 0.826 1.089

CSH_B4a|t1 0.227 0.057 3.978 Inf 0.000 0.115 0.339

CSH_B4a|t2 0.543 0.060 9.079 Inf 0.000 0.426 0.660

CSH_B5a|t1 0.316 0.058 5.485 Inf 0.000 0.203 0.429

CSH_B5a|t2 0.707 0.062 11.399 Inf 0.000 0.585 0.828

CSH_S10a|t1 0.433 0.059 7.388 Inf 0.000 0.318 0.548

CSH_S10a|t2 1.117 0.072 15.564 Inf 0.000 0.976 1.258

CSH_S19a|t1 0.735 0.063 11.642 Inf 0.000 0.611 0.859

CSH_S19a|t2 1.981 0.129 15.310 Inf 0.000 1.727 2.234

CSH_W2a|t1 0.500 0.060 8.397 Inf 0.000 0.383 0.617

CSH_W2a|t2 1.406 0.083 17.008 Inf 0.000 1.244 1.568

CSH_S7a|t1 0.731 0.062 11.693 Inf 0.000 0.608 0.853

CSH_S7a|t2 2.133 0.141 15.151 Inf 0.000 1.857 2.409

CSH_S8a|t1 -0.373 0.058 -6.408 Inf 0.000 -0.487 -0.259

CSH_S8a|t2 0.778 0.063 12.274 Inf 0.000 0.654 0.902

CSH_W1a|t1 -0.269 0.058 -4.667 Inf 0.000 -0.382 -0.156

CSH_W1a|t2 0.813 0.064 12.647 Inf 0.000 0.687 0.940

CSH_M7a|t1 0.695 0.062 11.165 Inf 0.000 0.573 0.817

CSH_M7a|t2 1.598 0.095 16.869 Inf 0.000 1.412 1.783

CSH_M6a|t1 0.655 0.062 10.619 Inf 0.000 0.534 0.776

CSH_M6a|t2 1.591 0.094 16.917 Inf 0.000 1.407 1.775

CSH_M4a|t1 0.234 0.058 4.075 Inf 0.000 0.122 0.347

CSH_M4a|t2 1.673 0.099 16.879 Inf 0.000 1.479 1.867

CSH_D3a|t1 -0.263 0.059 -4.465 Inf 0.000 -0.378 -0.148

CSH_D3a|t2 1.553 0.096 16.152 6322.319 0.000 1.365 1.742

CSH_M5a|t1 -0.130 0.057 -2.278 Inf 0.023 -0.241 -0.018

CSH_M5a|t2 0.954 0.067 14.142 Inf 0.000 0.822 1.086

CSH_M2a|t1 0.634 0.061 10.359 Inf 0.000 0.514 0.755

CSH_M2a|t2 1.466 0.086 16.997 Inf 0.000 1.297 1.635

Variances:

Estimate Std.Err t-value df P(>|t|) ci.lower ci.upper

.CSH_B3a 0.689 0.689 0.689

.CSH_S4a -0.135 -0.135 -0.135

.CSH_S5a 0.578 0.578 0.578

.CSH_S2a 0.299 0.299 0.299

.CSH_B11a 0.542 0.542 0.542

.CSH_B2a 0.579 0.579 0.579

.CSH_B8a 0.221 0.221 0.221

.CSH_B13a 0.407 0.407 0.407

.CSH_B4a 0.014 0.014 0.014

.CSH_B5a 0.268 0.268 0.268

.CSH_S10a 0.724 0.724 0.724

.CSH_S19a 0.624 0.624 0.624

.CSH_W2a 0.322 0.322 0.322

.CSH_S7a 0.760 0.760 0.760

.CSH_S8a 0.631 0.631 0.631

.CSH_W1a 0.453 0.453 0.453

.CSH_M7a 0.440 0.440 0.440

.CSH_M6a 0.275 0.275 0.275

.CSH_M4a 0.631 0.631 0.631

.CSH_D3a 0.854 0.854 0.854

.CSH_M5a 0.250 0.250 0.250

.CSH_M2a 0.165 0.165 0.165

A 1.000 1.000 1.000

B 1.000 1.000 1.000

C 1.000 1.000 1.000

D 1.000 1.000 1.000

G 1.000 1.000 1.000

Scales y*:

Estimate Std.Err t-value df P(>|t|) ci.lower ci.upper

CSH_B3a 1.000 1.000 1.000

CSH_S4a 1.000 1.000 1.000

CSH_S5a 1.000 1.000 1.000

CSH_S2a 1.000 1.000 1.000

CSH_B11a 1.000 1.000 1.000

CSH_B2a 1.000 1.000 1.000

CSH_B8a 1.000 1.000 1.000

CSH_B13a 1.000 1.000 1.000

CSH_B4a 1.000 1.000 1.000

CSH_B5a 1.000 1.000 1.000

CSH_S10a 1.000 1.000 1.000

CSH_S19a 1.000 1.000 1.000

CSH_W2a 1.000 1.000 1.000

CSH_S7a 1.000 1.000 1.000

CSH_S8a 1.000 1.000 1.000

CSH_W1a 1.000 1.000 1.000

CSH_M7a 1.000 1.000 1.000

CSH_M6a 1.000 1.000 1.000

CSH_M4a 1.000 1.000 1.000

CSH_D3a 1.000 1.000 1.000

CSH_M5a 1.000 1.000 1.000

CSH_M2a 1.000 1.000 1.000

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Terrence Jorgensen

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Nov 18, 2019, 8:32:12 AM11/18/19

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