Skip to contents

Convert an Estimates Table to a List of Data Frames

parameterEstimates_table_list.Rd

Create a list of data frames from the output of lavaan::parameterEstimates(), formatted in nearly the same way the argument output = "text" does.

Usage

parameterEstimates_table_list(
  object,
  ...,
  fit_object = NULL,
  se_also_to_na = character(0),
  se_not_to_na = character(0),
  drop_cols = "std.nox",
  rename_cols = character(0),
  est_funs = list(),
  header_funs = list(),
  footer_funs = list(),
  est_funs_args = NULL,
  header_funs_args = NULL,
  footer_funs_args = NULL
)

print_parameterEstimates_table_list(
  x,
  nd = 3,
  by_group = TRUE,
  drop_cols = character(0),
  na_str = " "
)

Arguments

object

It can a data frame similar in form to the output of lavaan::parameterEstimates(), or a lavaan object (e.g., the output of lavaan::sem()). If it is a lavaan object, then lavaan::parameterEstimates() will be called to generate the parameter estimates table.

...

If object is a lavaan object, then these are the optional arguments to be passed to lavaan::parameterEstimates() when it is called.

fit_object

(Optional). The lavaan object for getting additional information, if they are not available in object, and added as attributes to object. It essentially does what lavaan::parameterEstimates() does when setting output to "text".

se_also_to_na

Columns for which cells will be set to NA if the standard error of a parameter is zero, which is assumed to mean that this parameter is fixed. By default, these columns are included and no need to specify them for this argument: "z", "pvalue", "t", "df", "ci.lower", and "ci.upper". To exclude one of these columns from se_als_to_na, add it to se_not_to_na.

se_not_to_na

Columns for which cells will not be set to NA even if the standard error of a parameter is zero. Column names that appear here override se_also_to_na. Therefore, if "z", "pvalue", "t", "df", "ci.lower", and "ci.upper" are included in this argument, they will also not be set to NA.

drop_cols

The names of columns to be dropped from the printout. It can be the names after being renamed by rename_cols, or the original names before being renamed (i.e., the names in object), provided that the names in object are stored in the attribute "original_name" of each column, which is done by default by parameterEstimates_table_list().

rename_cols

If any columns are to be renamed, this is named character vector, with the names being the original names and the values being the new names. For example, c("pvalue" = "P(|>z|)") renames the column "pvalue" to "P(|z|)". It is recommended to quote the names too because they may not be standard names.

est_funs

If supplied, it should be a list of functions to be applied to each parameter estimates table, applied in the same order they appear in the list. It can be used create new columns or modify existing columns. Usually, this should be done before calling parameterEstimates_table_list() but provided as an option.

header_funs

If supplied, it should be a list of functions to be applied to object to generate the header sections. See Details on the expected format of the output of these functions.

If supplied, it should be a list of functions to be applied to object to generate the footer sections. See Details on the expected format of the output of these functions.

est_funs_args

If supplied, it must be a "list of list(s)". The length of this list must be equal to the number of functions in est_funs. Each sub-list is the list of arguments to be used when calling a function in est_funs. It must be an empty list() if no additional arguments are to be used when calling a function in est_funs.

header_funs_args

If supplied, it must be a "list of list(s)". The length of this list must be equal to the number of functions in header_funs. Each sub-list is the list of arguments to be used when calling a function in header_funs. It must be an empty list() if no additional arguments are to be used when calling a function in header_funs.

If supplied, it must be a "list of list(s)". The length of this list must be equal to the number of functions in footer_funs. Each sub-list is the list of arguments to be used when calling a function in footer_funs. It must be an empty list() if no additional arguments are to be used when calling a function in footer_funs.

x

The object to be printed. Should be the output of parameterEstimates_table_list().

nd

The number of decimal places to be displayed for numeric cells.

by_group

If TRUE, the default, tables will be grouped by groups first, and then by grouped by sections (e.g., Latent Variables, Regressions, etc.). If FALSE, then the tables will be grouped by sections first, and then grouped by groups. No effect if the number of groups is equal to one.

na_str

The string to be used for cells with NA. Default is " ", a white space.

Value

parameterEstimates_table_list()

A list of data frames of the class parameterEstimates_table_list, with this structure.

  • group: A list of data frames for each group. It is a list of length equal to one if the model has only one group. For each group, the content is a list of data frames, one for each section of the estimates.

  • model: A list of tables for sections such as user-defined parameters ("Defined Parameters") or model constraints ("Constraints").

  • header: A list of header sections.

  • footer: A list of footer sections.

The decision of not having a print method is intentional. It is intended to be used by other the print methods of other classes, to create the formatted list of tables, and then print it by calling print_parameterEstimates_table_list() internally.

print_parameterEstimates_table_list()

The original input, x, is returned invisibly. Called for its side effect to print the content of x.

Details

This function creates an output mimicking the output format when lavaan::parameterEstimates() is called with output set to "text". It only creates the output as a list of data frames, grouped in sections like Latent Variables and Regression, as in the printout of lavaan::parameterEstimates(). It does not format the content. The actual printing is to be done by print_parameterEstimates_table_list(), which will format the cells before printing them.

This function is not intended to be used by end-users. It is intended to be used inside other functions, such as a print method. Functions that add columns to the parameter estimates table of a lavaan object can use it and PRINT_parameterEstimates_table_list() to print the output in the lavaan-style, but with columns modified as needed and with additional header and/or footer sections added.

Therefore, it was developed with flexibility in mind, at the expense of user-friendliness.

If a list of functions is supplied to header_funs or footer_funs, they will be used to generate the headers and/or footers. The first argument of these function will be one of the followings.

If object is a data frame like object, then the first argument is this object when calling thews functions.

If object is a lavaan object, then the first argument is the parameter estimates table generated by lavaan::parameterEstimates() with output = "text", header = TRUE.

The output of these functions should be one of the following formats.

It can be a data frame with two optional attributes: section_title and print_args. If section_title is not null, it will be printed by cat() before printing tbe section. The header or footer section will then be printed by print(). If print_args is set to be a list of named arguments, then they will be used when calling print(). For example, setting print_args to list(right = FALSE, row.names = FALSE) will print the data frame with these arguments.

It can also be any other object that can be printed. One possible case is a character vector of footnotes. In this case, we can add this attribute print_fun and set it to "cat", the name of the function to be used to print the section, and add the attribute print_args and set it to be a named list of arguments to be passed to print_fun.

Special treatment when print-fun is "cat"`:

  • The default of sep is "\n". To override this default, set the attribute print_args and set sep to something else.

  • Each element in the object, which should be a character vector, is processed by strwrap() by default. Additional arguments to strwrap() can be passed by setting the attribute strwrap_args to a named list of the arguments for strwrap() (e.g., list(exdent = 2)). To disable this feature, set the attribute wrap_lines to FALSE.

These arguments header_funs and footer_args allow users to add header and footer sections and print them in the desired format.

Limitations

These function do not yet support multilevel models.

See also

print_parameterEstimates_table_list() for the printing function, and lavaan::parameterEstimates() for generating the parameter estimates table.

Author

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448

Examples


# Adapted from the help of lavaan::cfa()
library(lavaan)
#> This is lavaan 0.6-18
#> lavaan is FREE software! Please report any bugs.
mod <- "
visual  =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed   =~ x7 + x8 + x9
"
fit <- cfa(mod,
           data = HolzingerSwineford1939)
est <- parameterEstimates_table_list(fit,
                                     rename_cols = c("P(>|z|)" = "pvalue",
                                                     "S.E." = "SE"))
print_parameterEstimates_table_list(est,
                                    drop = "Z")
#> 
#> Parameter Estimates Settings:
#>                                              
#>  Standard errors:                  Standard  
#>  Information:                      Expected  
#>  Information saturated (h1) model: Structured
#> 
#> Latent Variables:
#>             Estimate    SE pvalue CI.Lo CI.Up
#>  visual =~                                   
#>   x1           1.000                         
#>   x2           0.554 0.100  0.000 0.358 0.749
#>   x3           0.729 0.109  0.000 0.516 0.943
#>  textual =~                                  
#>   x4           1.000                         
#>   x5           1.113 0.065  0.000 0.985 1.241
#>   x6           0.926 0.055  0.000 0.817 1.035
#>  speed =~                                    
#>   x7           1.000                         
#>   x8           1.180 0.165  0.000 0.857 1.503
#>   x9           1.082 0.151  0.000 0.785 1.378
#> 
#> Covariances:
#>             Estimate    SE pvalue CI.Lo CI.Up
#>  visual ~~                                   
#>   textual      0.408 0.074  0.000 0.264 0.552
#>   speed        0.262 0.056  0.000 0.152 0.373
#>  textual ~~                                  
#>   speed        0.173 0.049  0.000 0.077 0.270
#> 
#> Variances:
#>             Estimate    SE pvalue CI.Lo CI.Up
#>  .x1           0.549 0.114  0.000 0.326 0.772
#>  .x2           1.134 0.102  0.000 0.934 1.333
#>  .x3           0.844 0.091  0.000 0.667 1.022
#>  .x4           0.371 0.048  0.000 0.278 0.465
#>  .x5           0.446 0.058  0.000 0.332 0.561
#>  .x6           0.356 0.043  0.000 0.272 0.441
#>  .x7           0.799 0.081  0.000 0.640 0.959
#>  .x8           0.488 0.074  0.000 0.342 0.633
#>  .x9           0.566 0.071  0.000 0.427 0.705
#>   visual       0.809 0.145  0.000 0.524 1.094
#>   textual      0.979 0.112  0.000 0.760 1.199
#>   speed        0.384 0.086  0.000 0.215 0.553
fit2 <- cfa(mod,
            data = HolzingerSwineford1939,
            group = "school")
est2 <- parameterEstimates_table_list(fit2)
# The tables in the same group are printed together (default)
print_parameterEstimates_table_list(est2,
                                    by_group = TRUE)
#> 
#> Parameter Estimates Settings:
#>                                              
#>  Standard errors:                  Standard  
#>  Information:                      Expected  
#>  Information saturated (h1) model: Structured
#> 
#> Group 1 [Pasteur]:
#> Latent Variables:
#>             Estimate  S.E.      Z P(>|z|)  CI.Lo CI.Up
#>  visual =~                                            
#>   x1           1.000                                  
#>   x2           0.394 0.122  3.220   0.001  0.154 0.633
#>   x3           0.570 0.140  4.076   0.000  0.296 0.844
#>  textual =~                                           
#>   x4           1.000                                  
#>   x5           1.183 0.102 11.613   0.000  0.984 1.383
#>   x6           0.875 0.077 11.421   0.000  0.725 1.025
#>  speed =~                                             
#>   x7           1.000                                  
#>   x8           1.125 0.277  4.057   0.000  0.581 1.668
#>   x9           0.922 0.225  4.104   0.000  0.482 1.362
#> 
#> Group 1 [Pasteur]:
#> Covariances:
#>             Estimate  S.E.      Z P(>|z|)  CI.Lo CI.Up
#>  visual ~~                                            
#>   textual      0.479 0.106  4.531   0.000  0.272 0.686
#>   speed        0.185 0.077  2.397   0.017  0.034 0.337
#>  textual ~~                                           
#>   speed        0.182 0.069  2.628   0.009  0.046 0.317
#> 
#> Group 1 [Pasteur]:
#> Intercepts:
#>             Estimate  S.E.      Z P(>|z|)  CI.Lo CI.Up
#>  .x1           4.941 0.095 52.249   0.000  4.756 5.127
#>  .x2           5.984 0.098 60.949   0.000  5.792 6.176
#>  .x3           2.487 0.093 26.778   0.000  2.305 2.669
#>  .x4           2.823 0.092 30.689   0.000  2.642 3.003
#>  .x5           3.995 0.105 38.183   0.000  3.790 4.200
#>  .x6           1.922 0.079 24.321   0.000  1.767 2.077
#>  .x7           4.432 0.087 51.181   0.000  4.263 4.602
#>  .x8           5.563 0.078 71.214   0.000  5.410 5.716
#>  .x9           5.418 0.079 68.440   0.000  5.263 5.573
#>   visual       0.000                                  
#>   textual      0.000                                  
#>   speed        0.000                                  
#> 
#> Group 1 [Pasteur]:
#> Variances:
#>             Estimate  S.E.      Z P(>|z|)  CI.Lo CI.Up
#>  .x1           0.298 0.232  1.286   0.198 -0.156 0.753
#>  .x2           1.334 0.158  8.464   0.000  1.025 1.643
#>  .x3           0.989 0.136  7.271   0.000  0.723 1.256
#>  .x4           0.425 0.069  6.138   0.000  0.290 0.561
#>  .x5           0.456 0.086  5.292   0.000  0.287 0.624
#>  .x6           0.290 0.050  5.780   0.000  0.192 0.388
#>  .x7           0.820 0.125  6.580   0.000  0.576 1.065
#>  .x8           0.510 0.116  4.406   0.000  0.283 0.736
#>  .x9           0.680 0.104  6.516   0.000  0.476 0.885
#>   visual       1.097 0.276  3.967   0.000  0.555 1.639
#>   textual      0.894 0.150  5.963   0.000  0.600 1.188
#>   speed        0.350 0.126  2.778   0.005  0.103 0.596
#> 
#> Group 2 [Grant-White]:
#> Latent Variables:
#>             Estimate  S.E.      Z P(>|z|)  CI.Lo CI.Up
#>  visual =~                                            
#>   x1           1.000                                  
#>   x2           0.736 0.155  4.760   0.000  0.433 1.039
#>   x3           0.925 0.166  5.583   0.000  0.600 1.249
#>  textual =~                                           
#>   x4           1.000                                  
#>   x5           0.990 0.087 11.418   0.000  0.820 1.160
#>   x6           0.963 0.085 11.377   0.000  0.797 1.129
#>  speed =~                                             
#>   x7           1.000                                  
#>   x8           1.226 0.187  6.569   0.000  0.860 1.592
#>   x9           1.058 0.165  6.429   0.000  0.735 1.380
#> 
#> Group 2 [Grant-White]:
#> Covariances:
#>             Estimate  S.E.      Z P(>|z|)  CI.Lo CI.Up
#>  visual ~~                                            
#>   textual      0.408 0.098  4.153   0.000  0.215 0.600
#>   speed        0.276 0.076  3.639   0.000  0.127 0.425
#>  textual ~~                                           
#>   speed        0.222 0.073  3.022   0.003  0.078 0.365
#> 
#> Group 2 [Grant-White]:
#> Intercepts:
#>             Estimate  S.E.      Z P(>|z|)  CI.Lo CI.Up
#>  .x1           4.930 0.095 51.696   0.000  4.743 5.117
#>  .x2           6.200 0.092 67.416   0.000  6.020 6.380
#>  .x3           1.996 0.086 23.195   0.000  1.827 2.164
#>  .x4           3.317 0.093 35.625   0.000  3.135 3.500
#>  .x5           4.712 0.096 48.986   0.000  4.524 4.901
#>  .x6           2.469 0.094 26.277   0.000  2.285 2.653
#>  .x7           3.921 0.086 45.819   0.000  3.753 4.089
#>  .x8           5.488 0.087 63.174   0.000  5.318 5.659
#>  .x9           5.327 0.085 62.571   0.000  5.160 5.494
#>   visual       0.000                                  
#>   textual      0.000                                  
#>   speed        0.000                                  
#> 
#> Group 2 [Grant-White]:
#> Variances:
#>             Estimate  S.E.      Z P(>|z|)  CI.Lo CI.Up
#>  .x1           0.715 0.126  5.676   0.000  0.468 0.962
#>  .x2           0.899 0.123  7.339   0.000  0.659 1.139
#>  .x3           0.557 0.103  5.409   0.000  0.355 0.759
#>  .x4           0.315 0.065  4.870   0.000  0.188 0.442
#>  .x5           0.419 0.072  5.812   0.000  0.278 0.560
#>  .x6           0.406 0.069  5.880   0.000  0.271 0.541
#>  .x7           0.600 0.091  6.584   0.000  0.422 0.779
#>  .x8           0.401 0.094  4.249   0.000  0.216 0.586
#>  .x9           0.535 0.089  6.010   0.000  0.360 0.709
#>   visual       0.604 0.160  3.762   0.000  0.289 0.918
#>   textual      0.942 0.152  6.177   0.000  0.643 1.241
#>   speed        0.461 0.118  3.910   0.000  0.230 0.693
# The table are grouped by section then by group
print_parameterEstimates_table_list(est2,
                                    by_group = FALSE)
#> 
#> Parameter Estimates Settings:
#>                                              
#>  Standard errors:                  Standard  
#>  Information:                      Expected  
#>  Information saturated (h1) model: Structured
#> 
#> Latent Variables:
#> Group 1 [Pasteur]:
#>             Estimate  S.E.      Z P(>|z|)  CI.Lo CI.Up
#>  visual =~                                            
#>   x1           1.000                                  
#>   x2           0.394 0.122  3.220   0.001  0.154 0.633
#>   x3           0.570 0.140  4.076   0.000  0.296 0.844
#>  textual =~                                           
#>   x4           1.000                                  
#>   x5           1.183 0.102 11.613   0.000  0.984 1.383
#>   x6           0.875 0.077 11.421   0.000  0.725 1.025
#>  speed =~                                             
#>   x7           1.000                                  
#>   x8           1.125 0.277  4.057   0.000  0.581 1.668
#>   x9           0.922 0.225  4.104   0.000  0.482 1.362
#> 
#> Latent Variables:
#> Group 2 [Grant-White]:
#>             Estimate  S.E.      Z P(>|z|)  CI.Lo CI.Up
#>  visual =~                                            
#>   x1           1.000                                  
#>   x2           0.736 0.155  4.760   0.000  0.433 1.039
#>   x3           0.925 0.166  5.583   0.000  0.600 1.249
#>  textual =~                                           
#>   x4           1.000                                  
#>   x5           0.990 0.087 11.418   0.000  0.820 1.160
#>   x6           0.963 0.085 11.377   0.000  0.797 1.129
#>  speed =~                                             
#>   x7           1.000                                  
#>   x8           1.226 0.187  6.569   0.000  0.860 1.592
#>   x9           1.058 0.165  6.429   0.000  0.735 1.380
#> 
#> Covariances:
#> Group 1 [Pasteur]:
#>             Estimate  S.E.      Z P(>|z|)  CI.Lo CI.Up
#>  visual ~~                                            
#>   textual      0.479 0.106  4.531   0.000  0.272 0.686
#>   speed        0.185 0.077  2.397   0.017  0.034 0.337
#>  textual ~~                                           
#>   speed        0.182 0.069  2.628   0.009  0.046 0.317
#> 
#> Covariances:
#> Group 2 [Grant-White]:
#>             Estimate  S.E.      Z P(>|z|)  CI.Lo CI.Up
#>  visual ~~                                            
#>   textual      0.408 0.098  4.153   0.000  0.215 0.600
#>   speed        0.276 0.076  3.639   0.000  0.127 0.425
#>  textual ~~                                           
#>   speed        0.222 0.073  3.022   0.003  0.078 0.365
#> 
#> Intercepts:
#> Group 1 [Pasteur]:
#>             Estimate  S.E.      Z P(>|z|)  CI.Lo CI.Up
#>  .x1           4.941 0.095 52.249   0.000  4.756 5.127
#>  .x2           5.984 0.098 60.949   0.000  5.792 6.176
#>  .x3           2.487 0.093 26.778   0.000  2.305 2.669
#>  .x4           2.823 0.092 30.689   0.000  2.642 3.003
#>  .x5           3.995 0.105 38.183   0.000  3.790 4.200
#>  .x6           1.922 0.079 24.321   0.000  1.767 2.077
#>  .x7           4.432 0.087 51.181   0.000  4.263 4.602
#>  .x8           5.563 0.078 71.214   0.000  5.410 5.716
#>  .x9           5.418 0.079 68.440   0.000  5.263 5.573
#>   visual       0.000                                  
#>   textual      0.000                                  
#>   speed        0.000                                  
#> 
#> Intercepts:
#> Group 2 [Grant-White]:
#>             Estimate  S.E.      Z P(>|z|)  CI.Lo CI.Up
#>  .x1           4.930 0.095 51.696   0.000  4.743 5.117
#>  .x2           6.200 0.092 67.416   0.000  6.020 6.380
#>  .x3           1.996 0.086 23.195   0.000  1.827 2.164
#>  .x4           3.317 0.093 35.625   0.000  3.135 3.500
#>  .x5           4.712 0.096 48.986   0.000  4.524 4.901
#>  .x6           2.469 0.094 26.277   0.000  2.285 2.653
#>  .x7           3.921 0.086 45.819   0.000  3.753 4.089
#>  .x8           5.488 0.087 63.174   0.000  5.318 5.659
#>  .x9           5.327 0.085 62.571   0.000  5.160 5.494
#>   visual       0.000                                  
#>   textual      0.000                                  
#>   speed        0.000                                  
#> 
#> Variances:
#> Group 1 [Pasteur]:
#>             Estimate  S.E.      Z P(>|z|)  CI.Lo CI.Up
#>  .x1           0.298 0.232  1.286   0.198 -0.156 0.753
#>  .x2           1.334 0.158  8.464   0.000  1.025 1.643
#>  .x3           0.989 0.136  7.271   0.000  0.723 1.256
#>  .x4           0.425 0.069  6.138   0.000  0.290 0.561
#>  .x5           0.456 0.086  5.292   0.000  0.287 0.624
#>  .x6           0.290 0.050  5.780   0.000  0.192 0.388
#>  .x7           0.820 0.125  6.580   0.000  0.576 1.065
#>  .x8           0.510 0.116  4.406   0.000  0.283 0.736
#>  .x9           0.680 0.104  6.516   0.000  0.476 0.885
#>   visual       1.097 0.276  3.967   0.000  0.555 1.639
#>   textual      0.894 0.150  5.963   0.000  0.600 1.188
#>   speed        0.350 0.126  2.778   0.005  0.103 0.596
#> 
#> Variances:
#> Group 2 [Grant-White]:
#>             Estimate  S.E.      Z P(>|z|)  CI.Lo CI.Up
#>  .x1           0.715 0.126  5.676   0.000  0.468 0.962
#>  .x2           0.899 0.123  7.339   0.000  0.659 1.139
#>  .x3           0.557 0.103  5.409   0.000  0.355 0.759
#>  .x4           0.315 0.065  4.870   0.000  0.188 0.442
#>  .x5           0.419 0.072  5.812   0.000  0.278 0.560
#>  .x6           0.406 0.069  5.880   0.000  0.271 0.541
#>  .x7           0.600 0.091  6.584   0.000  0.422 0.779
#>  .x8           0.401 0.094  4.249   0.000  0.216 0.586
#>  .x9           0.535 0.089  6.010   0.000  0.360 0.709
#>   visual       0.604 0.160  3.762   0.000  0.289 0.918
#>   textual      0.942 0.152  6.177   0.000  0.643 1.241
#>   speed        0.461 0.118  3.910   0.000  0.230 0.693

# A simple function to add "***" for parameters with p-values < .001
add_sig <- function(object,
                    pvalue = "pvalue") {
    tmp <- object[, pvalue, drop = TRUE]
    if (!is.null(tmp)) {
        tmp[is.na(tmp)] <- 1
        tmp2 <- ifelse(tmp < .001, "***", "")
        i <- match(pvalue, colnames(object))
        out <- data.frame(object[, 1:i],
                          Sig = tmp2,
                          object[, seq(i + 1, ncol(object))])
      }
    out
  }

est3 <- parameterEstimates_table_list(fit2,
                                      est_funs = list(add_sig))
print_parameterEstimates_table_list(est3)
#> 
#> Parameter Estimates Settings:
#>                                              
#>  Standard errors:                  Standard  
#>  Information:                      Expected  
#>  Information saturated (h1) model: Structured
#> 
#> Group 1 [Pasteur]:
#> Latent Variables:
#>             Estimate  S.E.      Z P(>|z|) Sig  CI.Lo CI.Up
#>  visual =~                                                
#>   x1           1.000                                      
#>   x2           0.394 0.122  3.220   0.001      0.154 0.633
#>   x3           0.570 0.140  4.076   0.000 ***  0.296 0.844
#>  textual =~                                               
#>   x4           1.000                                      
#>   x5           1.183 0.102 11.613   0.000 ***  0.984 1.383
#>   x6           0.875 0.077 11.421   0.000 ***  0.725 1.025
#>  speed =~                                                 
#>   x7           1.000                                      
#>   x8           1.125 0.277  4.057   0.000 ***  0.581 1.668
#>   x9           0.922 0.225  4.104   0.000 ***  0.482 1.362
#> 
#> Group 1 [Pasteur]:
#> Covariances:
#>             Estimate  S.E.      Z P(>|z|) Sig  CI.Lo CI.Up
#>  visual ~~                                                
#>   textual      0.479 0.106  4.531   0.000 ***  0.272 0.686
#>   speed        0.185 0.077  2.397   0.017      0.034 0.337
#>  textual ~~                                               
#>   speed        0.182 0.069  2.628   0.009      0.046 0.317
#> 
#> Group 1 [Pasteur]:
#> Intercepts:
#>             Estimate  S.E.      Z P(>|z|) Sig  CI.Lo CI.Up
#>  .x1           4.941 0.095 52.249   0.000 ***  4.756 5.127
#>  .x2           5.984 0.098 60.949   0.000 ***  5.792 6.176
#>  .x3           2.487 0.093 26.778   0.000 ***  2.305 2.669
#>  .x4           2.823 0.092 30.689   0.000 ***  2.642 3.003
#>  .x5           3.995 0.105 38.183   0.000 ***  3.790 4.200
#>  .x6           1.922 0.079 24.321   0.000 ***  1.767 2.077
#>  .x7           4.432 0.087 51.181   0.000 ***  4.263 4.602
#>  .x8           5.563 0.078 71.214   0.000 ***  5.410 5.716
#>  .x9           5.418 0.079 68.440   0.000 ***  5.263 5.573
#>   visual       0.000                                      
#>   textual      0.000                                      
#>   speed        0.000                                      
#> 
#> Group 1 [Pasteur]:
#> Variances:
#>             Estimate  S.E.      Z P(>|z|) Sig  CI.Lo CI.Up
#>  .x1           0.298 0.232  1.286   0.198     -0.156 0.753
#>  .x2           1.334 0.158  8.464   0.000 ***  1.025 1.643
#>  .x3           0.989 0.136  7.271   0.000 ***  0.723 1.256
#>  .x4           0.425 0.069  6.138   0.000 ***  0.290 0.561
#>  .x5           0.456 0.086  5.292   0.000 ***  0.287 0.624
#>  .x6           0.290 0.050  5.780   0.000 ***  0.192 0.388
#>  .x7           0.820 0.125  6.580   0.000 ***  0.576 1.065
#>  .x8           0.510 0.116  4.406   0.000 ***  0.283 0.736
#>  .x9           0.680 0.104  6.516   0.000 ***  0.476 0.885
#>   visual       1.097 0.276  3.967   0.000 ***  0.555 1.639
#>   textual      0.894 0.150  5.963   0.000 ***  0.600 1.188
#>   speed        0.350 0.126  2.778   0.005      0.103 0.596
#> 
#> Group 2 [Grant-White]:
#> Latent Variables:
#>             Estimate  S.E.      Z P(>|z|) Sig  CI.Lo CI.Up
#>  visual =~                                                
#>   x1           1.000                                      
#>   x2           0.736 0.155  4.760   0.000 ***  0.433 1.039
#>   x3           0.925 0.166  5.583   0.000 ***  0.600 1.249
#>  textual =~                                               
#>   x4           1.000                                      
#>   x5           0.990 0.087 11.418   0.000 ***  0.820 1.160
#>   x6           0.963 0.085 11.377   0.000 ***  0.797 1.129
#>  speed =~                                                 
#>   x7           1.000                                      
#>   x8           1.226 0.187  6.569   0.000 ***  0.860 1.592
#>   x9           1.058 0.165  6.429   0.000 ***  0.735 1.380
#> 
#> Group 2 [Grant-White]:
#> Covariances:
#>             Estimate  S.E.      Z P(>|z|) Sig  CI.Lo CI.Up
#>  visual ~~                                                
#>   textual      0.408 0.098  4.153   0.000 ***  0.215 0.600
#>   speed        0.276 0.076  3.639   0.000 ***  0.127 0.425
#>  textual ~~                                               
#>   speed        0.222 0.073  3.022   0.003      0.078 0.365
#> 
#> Group 2 [Grant-White]:
#> Intercepts:
#>             Estimate  S.E.      Z P(>|z|) Sig  CI.Lo CI.Up
#>  .x1           4.930 0.095 51.696   0.000 ***  4.743 5.117
#>  .x2           6.200 0.092 67.416   0.000 ***  6.020 6.380
#>  .x3           1.996 0.086 23.195   0.000 ***  1.827 2.164
#>  .x4           3.317 0.093 35.625   0.000 ***  3.135 3.500
#>  .x5           4.712 0.096 48.986   0.000 ***  4.524 4.901
#>  .x6           2.469 0.094 26.277   0.000 ***  2.285 2.653
#>  .x7           3.921 0.086 45.819   0.000 ***  3.753 4.089
#>  .x8           5.488 0.087 63.174   0.000 ***  5.318 5.659
#>  .x9           5.327 0.085 62.571   0.000 ***  5.160 5.494
#>   visual       0.000                                      
#>   textual      0.000                                      
#>   speed        0.000                                      
#> 
#> Group 2 [Grant-White]:
#> Variances:
#>             Estimate  S.E.      Z P(>|z|) Sig  CI.Lo CI.Up
#>  .x1           0.715 0.126  5.676   0.000 ***  0.468 0.962
#>  .x2           0.899 0.123  7.339   0.000 ***  0.659 1.139
#>  .x3           0.557 0.103  5.409   0.000 ***  0.355 0.759
#>  .x4           0.315 0.065  4.870   0.000 ***  0.188 0.442
#>  .x5           0.419 0.072  5.812   0.000 ***  0.278 0.560
#>  .x6           0.406 0.069  5.880   0.000 ***  0.271 0.541
#>  .x7           0.600 0.091  6.584   0.000 ***  0.422 0.779
#>  .x8           0.401 0.094  4.249   0.000 ***  0.216 0.586
#>  .x9           0.535 0.089  6.010   0.000 ***  0.360 0.709
#>   visual       0.604 0.160  3.762   0.000 ***  0.289 0.918
#>   textual      0.942 0.152  6.177   0.000 ***  0.643 1.241
#>   speed        0.461 0.118  3.910   0.000 ***  0.230 0.693