If you have no full dataset, but you do have a sample covariance matrix, you can still fit your model. If you wish to add a mean structure, you need to provide a mean vector too. Importantly, if only sample statistics are provided, you must specify the number of observations that were used to compute the sample moments. The following example illustrates the use of a sample covariance matrix as input. First, we read in the lower half of the covariance matrix (including the diagonal):

lower <- '
 11.834
  6.947   9.364
  6.819   5.091  12.532
  4.783   5.028   7.495   9.986
 -3.839  -3.889  -3.841  -3.625  9.610
-21.899 -18.831 -21.748 -18.775 35.522 450.288 '

wheaton.cov <- 
    getCov(lower, names = c("anomia67", "powerless67", 
                            "anomia71", "powerless71",
                            "education", "sei"))

The getCov() function makes it easy to create a full covariance matrix (including variable names) if you only have the lower-half elements (perhaps pasted from a textbook or a paper). Note that the lower-half elements are written between two single quotes. Therefore, you have some additional flexibility. You can add comments, and blank lines. If the numbers are separated by a comma, or a semi-colon, that is fine too. For more information about getCov(), see the online manual page.

Next, we can specify our model, estimate it, and request a summary of the results:

# classic wheaton et al. model
wheaton.model <- '
  # latent variables
    ses     =~ education + sei
    alien67 =~ anomia67 + powerless67
    alien71 =~ anomia71 + powerless71
  # regressions
    alien71 ~ alien67 + ses
    alien67 ~ ses
  # correlated residuals
    anomia67 ~~ anomia71
    powerless67 ~~ powerless71
'
fit <- sem(wheaton.model, 
           sample.cov = wheaton.cov, 
           sample.nobs = 932)
summary(fit, standardized = TRUE)

lavaan 0.6-11 ended normally after 84 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        17
                                                      
  Number of observations                           932
                                                      
Model Test User Model:
                                                      
  Test statistic                                 4.735
  Degrees of freedom                                 4
  P-value (Chi-square)                           0.316

Parameter Estimates:

  Standard errors                             Standard
  Information                                 Expected
  Information saturated (h1) model          Structured

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  ses =~                                                                
    education         1.000                               2.607    0.842
    sei               5.219    0.422   12.364    0.000   13.609    0.642
  alien67 =~                                                            
    anomia67          1.000                               2.663    0.774
    powerless67       0.979    0.062   15.895    0.000    2.606    0.852
  alien71 =~                                                            
    anomia71          1.000                               2.850    0.805
    powerless71       0.922    0.059   15.498    0.000    2.628    0.832

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  alien71 ~                                                             
    alien67           0.607    0.051   11.898    0.000    0.567    0.567
    ses              -0.227    0.052   -4.334    0.000   -0.207   -0.207
  alien67 ~                                                             
    ses              -0.575    0.056  -10.195    0.000   -0.563   -0.563

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
 .anomia67 ~~                                                           
   .anomia71          1.623    0.314    5.176    0.000    1.623    0.356
 .powerless67 ~~                                                        
   .powerless71       0.339    0.261    1.298    0.194    0.339    0.121

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .education         2.801    0.507    5.525    0.000    2.801    0.292
   .sei             264.597   18.126   14.597    0.000  264.597    0.588
   .anomia67          4.731    0.453   10.441    0.000    4.731    0.400
   .powerless67       2.563    0.403    6.359    0.000    2.563    0.274
   .anomia71          4.399    0.515    8.542    0.000    4.399    0.351
   .powerless71       3.070    0.434    7.070    0.000    3.070    0.308
    ses               6.798    0.649   10.475    0.000    1.000    1.000
   .alien67           4.841    0.467   10.359    0.000    0.683    0.683
   .alien71           4.083    0.404   10.104    0.000    0.503    0.503

The sample.cov.rescale argument

If the estimator is ML (the default), then the sample variance-covariance matrix will be rescaled by a factor (N-1)/N. The reasoning is the following: the elements in a sample variance-covariance matrix have (usually) been divided by N-1. But the (normal-based) ML estimator would divide the elements by N. Therefore, we need to rescale. If you don’t want this to happen (for example in a simulation study), you can provide the argument sample.cov.rescale = FALSE.

Multiple groups

If you have multiple groups, the sample.cov argument must be a list containing the sample variance-covariance matrix of each group as a separate element in the list. If a mean structure is needed, the sample.mean argument must be a list containing the sample means of each group. Finally, the sample.nobs argument can be either a list or an integer vector containing the number of observations for each group.