categorial variariable in sem no standard error

[Mango Dada]

Dear all,

I am trying to compute a structural equation model with the sem-function in lavaan.
There are two categorial variables (one latent exogenous and one latent endogenous) I wish to include in the final version of the model.
As soon as I include one of the categorial variables in the model, however, R produces the following warning:

1: In estimateVCOV(lavaanModel, samplestats = lavaanSampleStats, options = lavaanOptions,  :
  lavaan WARNING: could not compute standard errors!

2: In computeTestStatistic(lavaanModel, partable = lavaanParTable,  :
  lavaan WARNING: could not compute scaled test statistic

Here is the code and the output:
(This is a very small version of the final model and here I introduce only one categorial variable. The warning is the same for the complex and any simple version of the model).

model1 <- '
# measurement models
#uv
Wertschaetzung_Essen =~ abwechslungsreiche_M + schnell_zubereitbar + koche_sehr_gerne + koche_sehr_haeufig

#av
Fleischverzicht =~ Ern_Index1

#structural part
Fleischverzicht ~ Wertschaetzung_Essen
'

fit_model1 <- sem(model1, data=survey2_subset, ordered = c("Ern_Index1"))
summary(fit_model1, fit.measures = TRUE, standardized=TRUE)

lavaan (0.5-15) converged normally after  31 iterations

                                                  Used       Total
  Number of observations                          3469        3676

  Estimator                                       DWLS      Robust
  Minimum Function Test Statistic               13.716          NA
  Degrees of freedom                                 4           4
  P-value (Chi-square)                           0.008          NA
  Scaling correction factor                                     NA
  Shift parameter                                    
    for simple second-order correction (Mplus variant)

Model test baseline model:

  Minimum Function Test Statistic             2176.159    1582.139
  Degrees of freedom                                10          10
  P-value                                        0.000       0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.996          NA
  Tucker-Lewis Index (TLI)                       0.989          NA

Root Mean Square Error of Approximation:

  RMSEA                                          0.026          NA
  90 Percent Confidence Interval          0.012  0.042          NA     NA
  P-value RMSEA <= 0.05                          0.994          NA

Parameter estimates:

  Information                                 Expected
  Standard Errors                           Robust.sem

                   Estimate  Std.err  Z-value  P(>|z|)   Std.lv  Std.all
Latent variables:
  Wertschaetzung_Essen =~
    abwchslngsr_M     1.000                               0.363    0.436
    schnll_zbrtbr     1.179                               0.428    0.438
    koche_shr_grn     2.549                               0.925    0.846
    koche_shr_hfg     2.530                               0.918    0.775
  Fleischverzicht =~
    Ern_Index1        1.000                               0.249    0.249

Regressions:
  Fleischverzicht ~
    Wrtschtzng_Es     0.302                               0.440    0.440

Intercepts:
    abwchslngsr_M     3.133                               3.133    3.760
    schnll_zbrtbr     1.701                               1.701    1.741
    koche_shr_grn     2.978                               2.978    2.725
    koche_shr_hfg     2.543                               2.543    2.148
    Wrtschtzng_Es     0.000                               0.000    0.000
    Fleischvrzcht     0.000                               0.000    0.000

Thresholds:
    Ern_Index1|t1     0.197                               0.197    0.197

Variances:
    abwchslngsr_M     0.562                               0.562    0.810
    schnll_zbrtbr     0.771                               0.771    0.808
    koche_shr_grn     0.339                               0.339    0.284
    koche_shr_hfg     0.559                               0.559    0.399
    Ern_Index1        0.938                               0.938    0.938
    Wrtschtzng_Es     0.132                               1.000    1.000
    Fleischvrzcht     0.050                               0.806    0.806

I suppose that the model is not identified, but there should be enough degrees of freedom and the loadings of the first manifest items are set to one as well.
What to do and try next?
I would be very grateful, if someone could help me or give me a hint what to do to make the model estimable with standard errors and a scaled test statistic.

Thanks very much in advance

Sandra

[Alex Schoemann]

Hi Sandra,

Your model is globally identified (positive df) but the latent variable Fleischvrzcht is not locally identified. For a latent variable with a single indicator, you must fix two parameters associated with the latent variable. Currently the factor loading is fixed to 1 to set the scale but you're estimating the residual variance and the latent variance. Fixing one of these parameters (e.g. fixing the residual variance of Ern_Index1 to 0) should help.

Alex

[yrosseel]

On 04/08/2014 11:14 AM, Mango Dada wrote:
> Fleischverzicht =~ Ern_Index1

This is the problem. This would work out-of-the-box if Ern_Index1 was a
continuous variable (because lavaan would set the residual variance of
Ern_Index1 to zero behind the scenes). But if fails if Ern_Index1 is a
categorical variable.

Simply remove this line, and replace all occurrences of
'Fleischverzicht' by 'Ern_Index1' in the other equations.

Yves.

[Amanda Pollitt]

How would using a categorical single indicator in the cfa function work? 

[yrosseel]

On 06/19/2014 12:06 AM, Amanda Pollitt wrote:
> How would using a categorical single indicator in the cfa function work?

I don't think that is possible. With a continuous indicator, we could
fix the residual error variance to a constant (perhaps zero), but with a
categorical indicator, the residual variance is not a free parameter. It
is a function of other parameters.

Yves.

[ni wi]

Hello! 

I'm new to R (and to SEM in general), and currently I'm trying to run a few CFAs.

I've came across similar warnings when I tried to fit a bifactor model to my data. I was able to fit more simple models, in which I've separated the factors for the bifactor model. 

here is the syntax and part of the output:

datar.model<- '

general =~ Q2 + Q3 + Q5 + Q8 + Q10 + Q11 + Q12 + Q15 + Q16 + Q18 + Q21 + Q22 + Q25 + Q28 + Q29 + Q30 + Q33 + Q35 + Q36 + Q37 + Q39 + Q40 + Q41 + Q43 + Q48 + Q49 + Q4 + Q7 + Q9 + Q13 + Q17 + Q20 + Q23 + Q26 + Q27 + Q31 + Q34 + Q38 + Q42 + Q44 + Q45 + Q46 + Q47

at =~ Q2 + Q3 + Q5 + Q8 + Q10 + Q11 + Q12 + Q15 + Q16 + Q18 + Q21 + Q22 + Q25 + Q28 + Q29 + Q30 + Q33 + Q35 + Q36 + Q37 + Q39 + Q40 + Q41 + Q43 + Q48 + Q49 

hy =~ Q4 + Q7 + Q9 + Q13 + Q17 + Q20 + Q23 + Q26 + Q27 + Q31 + Q34 + Q38 + Q42 + Q44 + Q45 + Q46 + Q47 

'

fit<- cfa (datar.model, data=datar, estimator="WLSMV", ordered=c("Q2", "Q3", "Q5", "Q8", "Q10", "Q11", "Q12", "Q15", "Q16", "Q18", "Q21", "Q22", "Q25", "Q28", "Q29", "Q30", "Q33", "Q35", "Q36", "Q37", "Q39", "Q40", "Q41", "Q43", "Q48", "Q49", "Q4", "Q7", "Q9", "Q13", "Q17", "Q20", "Q23", "Q26", "Q27", "Q31", "Q34", "Q38", "Q42", "Q44", "Q45", "Q46", "Q47"))

summary(fit, fit.measures=TRUE, standardized=TRUE)

Warning messages:

1: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats,  :

  lavaan WARNING: could not compute standard errors!

2: In lav_model_test(lavmodel = lavmodel, lavpartable = lavpartable,  :

  lavaan WARNING: could not compute scaled test statistic

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

lavaan (0.5-16) converged normally after 113 iterations

  Number of observations                          2414

  Estimator                                       DWLS      Robust

  Minimum Function Test Statistic             8561.327          NA

  Degrees of freedom                               814         814

  P-value (Chi-square)                           0.000          NA

  Scaling correction factor                                     NA

  Shift parameter                                     

    for simple second-order correction (Mplus variant)

Model test baseline model:

  Minimum Function Test Statistic           314818.047   79538.667

  Degrees of freedom                               903         903

  P-value                                        0.000       0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.975          NA

  Tucker-Lewis Index (TLI)                       0.973          NA

Root Mean Square Error of Approximation:

  RMSEA                                          0.063          NA

  90 Percent Confidence Interval          0.062  0.064          NA     NA

  P-value RMSEA <= 0.05                          0.000          NA

Weighted Root Mean Square Residual:

  WRMR                                           2.882       2.882

Parameter estimates:

  Information                                 Expected

  Standard Errors                           Robust.sem

                   Estimate  Std.err  Z-value  P(>|z|)   Std.lv  Std.all

Latent variables:

  general =~

    Q2            1.000                               0.629    0.629

    Q3            1.189                               0.748    0.748

    Q5            1.439                               0.906    0.906

    Q8            0.996                               0.627    0.627

    Q10           1.299                               0.817    0.817

    Q11          1.162                               0.732    0.732

    Q12           1.354                               0.852    0.852

    Q15           1.272                               0.800    0.800

    Q16           1.053                               0.663    0.663

    Q18           1.154                               0.726    0.726

Is it possible I've missed something in the syntax? 

Any thought would be much a appreciated!

בתאריך יום שבת, 21 ביוני 2014 15:50:45 UTC+3, מאת Yves Rosseel:

[ni wi]

.

[Edward Rigdon]

Diana--

     If a common factor has 2 indicators, you do not need to constrain the Loadings to equality in order to achieve identification, as long as the factor covaries significantly with something else, like another common factor.  Unless those loading equality constraints for the factors with two indicators are based on prior knowledge, I would remove them.  Understand otherwise that the CFA function is imposing constraints of its own to achieve identification.  It is quite likely that those defaults along would achieve identification for you, without the steps you have taken in this syntax.  On the other hand, I am entirely in favor of specifying your own model, rather than relying on automatic constraints that may not be entirely clear.

--Ed Rigdon

Sent from my iPad

On Jun 25, 2014, at 4:18 PM, Diana Meter <djm...@gmail.com> wrote:

Hello,

I've been trying to fit a model with a number of single indicator and 2-indicator constructs. I also have a categorical single indicator, but I pulled it out just to see if I could get this to run. I previously fit this model in another program and had fair model fit. I am new to lavaan and have tried different ways of setting the scale and providing values for the variances and residual variances in order for each construct to be locally identified. After running the model below the following error message came up:

lavaan WARNING: covariance matrix of latent variables is not positive definite; use inspect(fit,"cov.lv") to investigate.

If anyone has ideas about how to fix this syntax or a better (or best) way model with single and 2-indicator constructs, I'd very much appreciate your response.
Thank you!

mod1 <- '

cvict =~ cvict1 + cvict2 + cvict3

cbul =~ v2*cbul1 + v2*cbul2

clim =~ clim1 + clim2 + clim3 + clim4

teachdo=~NA*teachdo1

peerdo=~NA*peerdo1

agg =~ v3*agg1 + v3*agg2

assert =~ v6*assert1 + v6*assert2

talk=~NA*talk1

telladult =~ v4*telladult1 + v4*telladult2

donothing =~ v5*donothing1 + v5*donothing2

cvict~~1*cvict

clim~~1*clim

teachdo~~1*teachdo

peerdo~~1*peerdo

agg~~1*agg

assert~~1*assert

talk~~1*talk

telladult~~1*telladult

cbul~~1*cbul

donothing~~1*donothing'

fit1 <- cfa(mod1, data=data, meanstructure=T, control=list(iter.max=1000), verbose=TRUE, std.lv=TRUE)

summary(fit1, standardized=T, fit.measures=T)

Warning message:

In lavaan::lavaan(model = mod1, data = data, meanstructure = T,  :

 

> summary(fit1, standardized=T, fit.measures=T)

lavaan (0.5-16) converged normally after  45 iterations

  Number of observations                           480

  Estimator                                         ML

  Minimum Function Test Statistic              527.746

  Degrees of freedom                               133

  P-value (Chi-square)                           0.000

Model test baseline model:

  Minimum Function Test Statistic             2369.511

  Degrees of freedom                               190

  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.819

  Tucker-Lewis Index (TLI)                       0.741

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)             -13373.637

  Loglikelihood unrestricted model (H1)     -13109.764

  Number of free parameters                         97

  Akaike (AIC)                               26941.274

  Bayesian (BIC)                             27346.131

  Sample-size adjusted Bayesian (BIC)        27038.263

Root Mean Square Error of Approximation:

  RMSEA                                          0.079

  90 Percent Confidence Interval          0.072  0.086

  P-value RMSEA <= 0.05                          0.000

Standardized Root Mean Square Residual:

  SRMR                                           0.067

Parameter estimates:

  Information                                 Expected

  Standard Errors                             Standard

                   Estimate  Std.err  Z-value  P(>|z|)   Std.lv  Std.all

Latent variables:

  cvict =~

    cvict1            0.246    0.037    6.684    0.000    0.246    0.399

    cvict2            0.427    0.046    9.321    0.000    0.427    0.653

    cvict3            0.151    0.026    5.716    0.000    0.151    0.339

  cbul =~

    cbul1    (v2)     0.236    0.018   13.435    0.000    0.236    0.511

    cbul2    (v2)     0.236    0.018   13.435    0.000    0.236    0.626

  clim =~

    clim1             0.727    0.070   10.350    0.000    0.727    0.498

    clim2             0.522    0.076    6.895    0.000    0.522    0.336

    clim3             0.863    0.082   10.486    0.000    0.863    0.504

    clim4             0.777    0.073   10.667    0.000    0.777    0.513

  teachdo =~

    teachdo1          1.819    0.059   30.984    0.000    1.819    1.000

  peerdo =~

    peerdo1           1.612    0.052   30.984    0.000    1.612    1.000

  agg =~

    agg1     (v3)     0.770    0.040   19.092    0.000    0.770    0.726

    agg2     (v3)     0.770    0.040   19.092    0.000    0.770    0.667

  assert =~

    assert1  (v6)     0.817    0.053   15.543    0.000    0.817    0.657

    assert2  (v6)     0.817    0.053   15.543    0.000    0.817    0.575

  talk =~

    talk1             1.267    0.041   30.984    0.000    1.267    1.000

  telladult =~

    telldlt1 (v4)     1.285    0.044   28.938    0.000    1.285    0.958

    telldlt2 (v4)     1.285    0.044   28.938    0.000    1.285    0.914

  donothing =~

    donthng1 (v5)     0.565    0.060    9.465    0.000    0.565    0.437

    donthng2 (v5)     0.565    0.060    9.465    0.000    0.565    0.506

Covariances:

  cvict ~~

    cbul              0.634    0.086    7.392    0.000    0.634    0.634

    clim             -0.302    0.085   -3.555    0.000   -0.302   -0.302

    teachdo          -0.239    0.062   -3.840    0.000   -0.239   -0.239

    peerdo           -0.045    0.064   -0.709    0.479   -0.045   -0.045

    agg               0.000    0.078    0.003    0.997    0.000    0.000

    assert            0.094    0.085    1.101    0.271    0.094    0.094

    talk              0.120    0.063    1.891    0.059    0.120    0.120

    telladult         0.036    0.065    0.552    0.581    0.036    0.036

    donothing        -0.011    0.105   -0.109    0.913   -0.011   -0.011

  cbul ~~

    clim             -0.152    0.088   -1.734    0.083   -0.152   -0.152

    teachdo          -0.166    0.064   -2.610    0.009   -0.166   -0.166

    peerdo           -0.119    0.064   -1.862    0.063   -0.119   -0.119

    agg               0.276    0.078    3.553    0.000    0.276    0.276

    assert           -0.102    0.086   -1.183    0.237   -0.102   -0.102

    talk              0.088    0.064    1.362    0.173    0.088    0.088

    telladult        -0.110    0.066   -1.659    0.097   -0.110   -0.110

    donothing        -0.062    0.107   -0.585    0.559   -0.062   -0.062

  clim ~~

    teachdo           0.765    0.042   18.327    0.000    0.765    0.765

    peerdo            0.582    0.050   11.720    0.000    0.582    0.582

    agg               0.067    0.077    0.868    0.386    0.067    0.067

    assert            0.220    0.082    2.673    0.008    0.220    0.220

    talk              0.010    0.062    0.167    0.867    0.010    0.010

    telladult         0.461    0.056    8.200    0.000    0.461    0.461

    donothing         0.301    0.102    2.952    0.003    0.301    0.301

  teachdo ~~

    peerdo            0.354    0.040    8.875    0.000    0.354    0.354

    agg               0.071    0.056    1.260    0.208    0.071    0.071

    assert            0.001    0.061    0.015    0.988    0.001    0.001

    talk              0.041    0.046    0.902    0.367    0.041    0.041

    telladult         0.137    0.046    2.974    0.003    0.137    0.137

    donothing         0.101    0.075    1.336    0.181    0.101    0.101

  peerdo ~~

    agg               0.114    0.056    2.050    0.040    0.114    0.114

    assert            0.085    0.061    1.399    0.162    0.085    0.085

    talk              0.046    0.046    1.018    0.308    0.046    0.046

    telladult         0.381    0.040    9.423    0.000    0.381    0.381

    donothing         0.120    0.075    1.595    0.111    0.120    0.120

  agg ~~

    assert            0.194    0.074    2.614    0.009    0.194    0.194

    talk              0.093    0.056    1.653    0.098    0.093    0.093

    telladult        -0.062    0.058   -1.066    0.286   -0.062   -0.062

    donothing        -0.045    0.093   -0.479    0.632   -0.045   -0.045

  assert ~~

    talk              0.553    0.051   10.840    0.000    0.553    0.553

    telladult         0.292    0.060    4.868    0.000    0.292    0.292

    donothing        -0.295    0.100   -2.936    0.003   -0.295   -0.295

  talk ~~

    telladult         0.304    0.043    7.110    0.000    0.304    0.304

    donothing        -0.001    0.075   -0.010    0.992   -0.001   -0.001

  telladult ~~

    donothing         0.142    0.077    1.827    0.068    0.142    0.142

Intercepts:

    cvict1            1.264    0.028   44.845    0.000    1.264    2.047

    cvict2            1.354    0.030   45.396    0.000    1.354    2.072

    cvict3            1.096    0.020   53.921    0.000    1.096    2.461

    cbul1             1.168    0.021   55.325    0.000    1.168    2.525

    cbul2             1.128    0.017   65.422    0.000    1.128    2.986

    clim1             2.901    0.067   43.537    0.000    2.901    1.987

    clim2             2.851    0.071   40.167    0.000    2.851    1.833

    clim3             2.148    0.078   27.486    0.000    2.148    1.255

    clim4             2.021    0.069   29.227    0.000    2.021    1.334

    teachdo1          2.079    0.083   25.043    0.000    2.079    1.143

    peerdo1           1.766    0.074   24.001    0.000    1.766    1.095

    agg1              1.619    0.048   33.429    0.000    1.619    1.526

    agg2              1.783    0.053   33.831    0.000    1.783    1.544

    assert1           3.416    0.057   60.139    0.000    3.416    2.745

    assert2           3.138    0.065   48.346    0.000    3.138    2.207

    talk1             2.879    0.058   49.791    0.000    2.879    2.273

    telladult1        2.436    0.061   39.774    0.000    2.436    1.815

    telladult2        2.497    0.064   38.905    0.000    2.497    1.776

    donothing1        2.791    0.059   47.312    0.000    2.791    2.159

    donothing2        2.243    0.051   43.982    0.000    2.243    2.008

    cvict             0.000                               0.000    0.000

    cbul              0.000                               0.000    0.000

    clim              0.000                               0.000    0.000

    teachdo           0.000                               0.000    0.000

    peerdo            0.000                               0.000    0.000

    agg               0.000                               0.000    0.000

    assert            0.000                               0.000    0.000

    talk              0.000                               0.000    0.000

    telladult         0.000                               0.000    0.000

    donothing         0.000                               0.000    0.000

Variances:

    cvict             1.000                               1.000    1.000

    clim              1.000                               1.000    1.000

    teachdo           1.000                               1.000    1.000

    peerdo            1.000                               1.000    1.000

    agg               1.000                               1.000    1.000

    assert            1.000                               1.000    1.000

    talk              1.000                               1.000    1.000

    telladult         1.000                               1.000    1.000

    cbul              1.000                               1.000    1.000

    donothing         1.000                               1.000    1.000

    cvict1            0.321    0.024                      0.321    0.841

    cvict2            0.245    0.036                      0.245    0.573

    cvict3            0.176    0.013                      0.176    0.885

    cbul1             0.158    0.012                      0.158    0.739

    cbul2             0.087    0.009                      0.087    0.608

    clim1             1.603    0.114                      1.603    0.752

    clim2             2.145    0.142                      2.145    0.887

    clim3             2.186    0.156                      2.186    0.746

    clim4             1.692    0.121                      1.692    0.737

    teachdo1          0.000                               0.000    0.000

    peerdo1           0.000                               0.000    0.000

    agg1              0.533    0.058                      0.533    0.474

    agg2              0.740    0.067                      0.740    0.555

    assert1           0.880    0.086                      0.880    0.568

    assert2           1.354    0.109                      1.354    0.670

    talk1             0.000                               0.000    0.000

    telladult1        0.149    0.037                      0.149    0.083

    telladult2        0.325    0.041                      0.325    0.165

    donothing1        1.351    0.107                      1.351    0.809

    donothing2        0.929    0.087                      0.929    0.744

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[yrosseel]

On 06/23/2014 01:08 PM, ni wi wrote:
> Hello!
> I'm new to R (and to SEM in general), and currently I'm trying to run a
> few CFAs.
> I've came across similar warnings when I tried to fit a bifactor model
> to my data. I was able to fit more simple models, in which I've
> separated the factors for the bifactor model.
>
> here is the syntax and part of the output:
>
> datar.model<- '
> general =~ Q2 + Q3 + Q5 + Q8 + Q10 + Q11 + Q12 + Q15 + Q16 + Q18 + Q21 +
> Q22 + Q25 + Q28 + Q29 + Q30 + Q33 + Q35 + Q36 + Q37 + Q39 + Q40 + Q41 +
> Q43 + Q48 + Q49 + Q4 + Q7 + Q9 + Q13 + Q17 + Q20 + Q23 + Q26 + Q27 + Q31
> + Q34 + Q38 + Q42 + Q44 + Q45 + Q46 + Q47
> at =~ Q2 + Q3 + Q5 + Q8 + Q10 + Q11 + Q12 + Q15 + Q16 + Q18 + Q21 + Q22
> + Q25 + Q28 + Q29 + Q30 + Q33 + Q35 + Q36 + Q37 + Q39 + Q40 + Q41 + Q43
> + Q48 + Q49
> hy =~ Q4 + Q7 + Q9 + Q13 + Q17 + Q20 + Q23 + Q26 + Q27 + Q31 + Q34 + Q38
> + Q42 + Q44 + Q45 + Q46 + Q47
> '

In a bifactor model, the 'general' factor should be orthogonal
(uncorrelated) to the other factors. So, add this:

general ~~ 0*at
general ~~ 0*hy

to your model syntax.

Yves.