Utility Functions For Covariance Matrices

Convenience functions to deal with covariance and correlation matrices.

Usage

lav_getcov(x, lower = TRUE, diagonal = TRUE, sds = NULL,
       names = paste("V", 1:nvar, sep=""))
getCov(x, lower = TRUE, diagonal = TRUE, sds = NULL,
       names = paste("V", 1:nvar, sep=""))
lav_char2num(s)
char2num(s)
lav_cor2cov(R, sds, names = NULL)
cor2cov(R, sds, names = NULL)

Arguments

x: The elements of the covariance matrix. Either inside a character string or as a numeric vector. In the former case, the function lav_char2num is used to convert the numbers (inside the character string) to numeric values.
lower: Logical. If TRUE, the numeric values in x are the lower-triangular elements of the (symmetric) covariance matrix only. If FALSE, x contains the upper triangular elements only. Note we always assumed the elements are provided row-wise!
diagonal: Logical. If TRUE, the numeric values in x include the diagonal elements. If FALSE, a unit diagonal is assumed.
sds: A numeric vector containing the standard deviations to be used to scale the elements in x or the correlation matrix R into a covariance matrix.
names: The variable names of the observed variables.
s: Character string containing numeric values; comma's and semi-colons are ignored.
R: A correlation matrix, to be scaled into a covariance matrix.

Details

The lav_getcov function is typically used to input the lower (or upper) triangular elements of a (symmetric) covariance matrix. In many examples found in handbooks, only those elements are shown. However, lavaan needs a full matrix to proceed.

The lav_cor2cov function is the inverse of the cov2cor function, and scales a correlation matrix into a covariance matrix given the standard deviations of the variables. Optionally, variable names can be given.

Examples

# The classic Wheaton et. al. (1977) model 
# panel data on he stability of alienation
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 '

# convert to a full symmetric covariance matrix with names
wheaton.cov <- lav_getcov(lower, names=c("anomia67","powerless67", "anomia71",
                                     "powerless71","education","sei"))

# the model
wheaton.model <- '
  # measurement model
    ses     =~ education + sei
    alien67 =~ anomia67 + powerless67
    alien71 =~ anomia71 + powerless71

  # equations
    alien71 ~ alien67 + ses
    alien67 ~ ses

  # correlated residuals
    anomia67 ~~ anomia71
    powerless67 ~~ powerless71
'

# fitting the model
fit <- sem(wheaton.model, sample.cov=wheaton.cov, sample.nobs=932)

# showing the results
summary(fit, standardized=TRUE)
#> lavaan 0.6-21 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
#>