# How to interpret this lavaan structural equation model?

I created following structural equation model from iris data set using lavaan package in R:

How do I interpret these numbers. The output (of sem() function of lavaan package) is given below. It did not give any P values:

lavaan (0.5-18) converged normally after  64 iterations

Number of observations                           150

Estimator                                         ML
Minimum Function Test Statistic                   NA
Degrees of freedom                                -4
Minimum Function Value               0.0000000000000

Parameter estimates:

Information                                 Expected
Standard Errors                             Standard

Estimate  Std.err  Z-value  P(>|z|)
Latent variables:
sepf =~
Sepal.Length      1.000
Sepal.Width      -0.469
petf =~
Petal.Length      1.000
Petal.Width       0.507
lenf =~
Petal.Length      1.000
Sepal.Length     -0.177
widf =~
Sepal.Width       1.000
strf =~
sepf              1.000
petf              2.084
bulkf =~
lenf              1.000
widf              0.579

Regressions:
strf ~
Species           0.842
bulkf ~
Species           0.290

Covariances:
strf ~~
bulkf             0.065

Variances:
Sepal.Length      0.361
Sepal.Width       0.129
Petal.Length      0.231
Petal.Width       0.047
sepf             -0.120
petf             -0.220
lenf             -0.179
widf              0.084
strf              0.053
bulkf            -0.025
-----------------------------------------------
Warning messages:
1: In lav_data_full(data = data, group = group, group.label = group.label,  :
lavaan WARNING: unordered factor(s) with more than 2 levels detected in data: Species
2: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats,  :
lavaan WARNING: could not compute standard errors!
lavaan NOTE: this may be a symptom that the model is not identified.

3: In lavaan::lavaan(model = model, data = mydf, model.type = "sem",  :
lavaan WARNING: some estimated variances are negative
4: In lavaan::lavaan(model = model, data = mydf, model.type = "sem",  :
lavaan WARNING: covariance matrix of latent variables is not positive definite; use inspect(fit,"cov.lv") to investigate.
5: In sqrt(ETA2) : NaNs produced
6: In sqrt(ETA2) : NaNs produced
7: In sqrt(ETA2) : NaNs produced
>


Do I just take large estimates as signficant? Thanks for your insight.

• Might be wrong, but propably the negative degrees of freedoms indicate that your model is underfitted and thus, the proposed model cannot be estimated/ tested. Therefore you cannot make any conclusions based on your model. If this is wrong, please correct me, statistics pros.
– Jens
Jun 19, 2015 at 19:19
• @Jens you're completely correct, this model is vastly over-identified and hence it is not unique (therefore, it's likelihood surface has no curvature, and no standard errors can be computed). The model converges to some location, but given some different starting values it will almost certainly converge to an entirely different location that fits equally well. Therefore, do not interpret this model at all, as it is largely meaningless, and lavaan surely printed a warning message saying that the model is probably not identified. Jun 19, 2015 at 20:08
• I have added the warnings that came with the output. Can we say if there is a particular latent factor or a particular association is completely wrong and the model should be retried after its removal? Also, there is warning that there are more than 2 levels in a factor (Spc or Species variable). So do I take that more than 2 factors are not allowed and I have to create dummy variables for such factor variables?
– rnso
Jun 20, 2015 at 0:16
• You really can't say anything at all about this model. On top of being completely unidentified it is badly broken (negative variance terms abound). So I would throw this model out and try something completely different. Jun 20, 2015 at 0:23
• The dashed lines appear to be fixed coefficients, which are often used for identifying latent variables (setting their metric). Jun 21, 2015 at 14:23