I am working with RStudio, but there are other options for running R. Here are the basic steps to get you started and run a cross-cultural equivalence test.

1. Set your working directory

This step is important because it will allow you to call your data file later on repeatedly without listing the whole path of where it is saved. For example, I saved the file that I am working with on my dropbox folder in a folder called ‘Stats’ that is in my ‘PDF’ folder.
I need to type this command:

setwd(“C:\\Users\\Ron\\Dropbox\\PDF\\Stats”)

Two important points:
a) for some strange reason you need double \\ to set your directory paths with windows.
b) make sure that there are no spaces in any of your file or directory paths. R does not like it and will throw a tantrum if you have a space somewhere.

2. Read your data into R

The most convenient way to read data into R is using .csv files. Any programme like SPSS or Excel will allow you to save your data as a .csv file. There are a few more things that we need to discuss about saving your data, but I will discuss this below.

Type:
justice <- read.csv(“justice.csv”, header = TRUE)

R is an object oriented language, which means we will constantly create objects by calling on functions: object <- function. This may seem weird at first, but will allow you to do lots of cool stuff in a very efficient way.

I am using a data that tested a justice scale, so I am calling my object ‘justice’.

3. Deal with missing data

If you have absolutely no missing data in your data file, skip this step. However most mortal researcher souls will have some missing data in their spreadsheet. R is very temperamental with missing data and we need to tell it what missing data is and how to deal with it. Some people (including myself) who are used to SPSS typically leave missing data as a blank cell in the spreadsheet. This will create problems. The best option is to write a little syntax command in spss to recode all blank cells to a constant number.
For example, I could write something like this in SPSS:

recode variable1 to variable12
(sysmis=9999) (else=copy) into
pj1 pj2 pj3 pj4 ij1 ij2 ij3 ij4 dj1 dj2 dj3 dj4.
Execute.

Now I can save those new variables as a .csv file and read into R using the step above.

Once you have executed step 2, you need to define these annoying 9999s as missing values.
The simplest and straightforward option is to write this short command that converts all these offending values into NA – the R form of missing data.

justice[justice==9999] <- NA

Note the square brackets and double ==. If you want to treat only a selected variable, you could write:

justice$pj1[justice$pj1==9999] <- NA

This tells R that you want only the pj1 variable in the dataframe justice to be treated in this way.

To check that all worked well, type:

summary(justice)

You should see something like this:

If all went well, now your minimum and maximum values are within the bounds of your original data and you have a row of NA’s a the bottom of each variable column.

4. Loading the analysis packages

R is a very powerful tool because it is constantly expanding. Researchers from around the world are uploading tools and packages that allow you to run fancy new stats all the time. However, the base installation of R does not include them. So we need to tell R which packages we want to use.
For measurement invariance tests, these three are particularly useful: lavaan (the key one) and semTools (important for the invariance tests).

Write this code to download and install the packages on your machine:

install.packages(c(“semTools”, “lavaan”))

Make sure you have good internet connectivity and you are not blocked by an institutional firewall. I had some problems recently trying to download R packages when accessing it from a university campus with a strong firewall.

Once all packages are downloaded, you need to call them before you can run any analyses:

library(“lavaan”)

library(“semTools”)

Important: You need to call these packages each time that you want to run some analyses, if you have restarted R or RStudio.

5. Running the analyses

R is an object oriented language, as I mentioned before. The analysis can be executed in a couple of steps. First we need to specify the model that we run by creating a new object that contains all the information. Then we tell R what to do with that model. Finally, we have various options for obtaining the results, that is the fit indices and parameter estimates as well as other diagnostic information.

Let’s create the model first:
cfa.justice<-‘
pj=~pj1+pj2+pj3+pj4
ij=~ij1+ij2+ij3+ij4
dj=~dj1+dj2+dj3+dj4’

This creates the model that we can then work with. The ‘=~’ denotes that the items are loading on the latent factor. This is what it looks like:

The next set of commands sets specifies what should be done with the model. In the case of a simple CFA, we can call this function:

fit.cfa <-cfa(cfa.justice, data=justice)

To identify the model, lavaan sets the loading of the first item on each latent variable to 1. This is convenient, but may be problematic if the item is not a good indicator. An alternative strategy is to set the variance of the latent variable to 1. This can be done by adding std.lv=TRUE to the fit statement.

fit.cfa <-cfa(cfa.justice, data=justice, std.lv=TRUE)

This statement runs the analysis, but we still need to request the output.

The simplest way is to use summary again. Here is an option that prints both the fit indices and the standardized parameters.

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

Here is a truncated and annotated version of the output:

lavaan (0.5-17) converged normally after  39 iterations
Used       Total

  Number of observations                          2518        2634

# The following shows the estimator and the Chi square stats. As can be seen, we have 51 df’s, but the model does not fit that well.

  Estimator                                                  ML

Minimum Function Test Statistic              686.657

Degrees of freedom                                   51

P-value (Chi-square)                                 0.000

Model test baseline model:
Minimum Function Test Statistic            20601.993

Degrees of freedom                                 66

P-value                                                     0.000

#The incremental fit indices are in contrast quite good. The CFI and TLI should be ideally be above .95 (or at least .90). So this model does look good.

User model versus baseline model:
Comparative Fit Index (CFI)                    0.969

Tucker-Lewis Index (TLI)                       0.960

Loglikelihood and Information Criteria:
Loglikelihood user model (H0)             -44312.277

Loglikelihood unrestricted model (H1)     -43968.949
Number of free parameters                         27

#The AIC and BIC are useful for comparing models, especially non-nested models. Not the case right now.

  Akaike (AIC)                               88678.555

Bayesian (BIC)                             88835.998

Sample-size adjusted Bayesian (BIC)        88750.212

#The RMSEA should be small. Values smaller than .08 are deemed acceptable, below .05 are good. We are doing ok-ish with this one here.

Root Mean Square Error of Approximation:
RMSEA                                          0.070

90 Percent Confidence Interval          0.066  0.075

P-value RMSEA <= 0.05                          0.000

#Another useful lack of fit index. The SRMR should be below .05 if possible. This is looking good.

Standardized Root Mean Square Residual:
SRMR                                           0.037

#Now we have a print out of all the parameter estimates, including the standardized loadings, variances and  covariances. Here it is important to check whether loadings are relatively even and strong, and that the variances and covariances are reasonable (e.g., we want to avoid very high correlations between latent variables). It is looking ok overall. Item ij4 may need some careful attention.

Parameter estimates:
Information             Expected  Standard Errors                             Standard
Estimate  Std.err  Z-value  P(>|z|)   Std.lv  Std.all

Latent variables:

pj =~    pj1   1.000                                           1.202    0.789

pj2               1.009    0.027   38.005    0.000    1.213    0.790

pj3               0.769    0.025   31.003    0.000    0.924    0.643

pj4               0.802    0.024   33.244    0.000    0.963    0.687

ij =~    ij1   1.000                                             1.256    0.879

ij2               1.064    0.014   75.039    0.000    1.335    0.957

ij3               1.015    0.015   68.090    0.000    1.274    0.910

ij4               0.808    0.022   37.412    0.000    1.014    0.644

dj =~    dj1 1.000                                              1.211    0.821

dj2               1.013    0.019   51.973    0.000    1.227    0.871

dj3               1.056    0.020   52.509    0.000    1.279    0.877

dj4               1.014    0.021   48.848    0.000    1.228    0.834
Covariances:

pj ~~    ij    0.828    0.041   20.435    0.000    0.549    0.549

dj                0.817    0.040   20.187    0.000    0.562    0.562

ij ~~    dj    0.711    0.037   19.005    0.000    0.467    0.467

Variances:

pj1               0.874    0.036                      0.874    0.377

pj2               0.889    0.036                      0.889    0.377

pj3               1.213    0.039                      1.213    0.587

pj4               1.040    0.035                      1.040    0.528

ij1               0.464    0.016                      0.464    0.227

ij2               0.164    0.011                      0.164    0.084

ij3               0.336    0.013                      0.336    0.172

ij4               1.448    0.042                      1.448    0.585

dj1               0.709    0.025                      0.709    0.326

dj2               0.479    0.019                      0.479    0.242

dj3               0.489    0.020                      0.489    0.230

dj4               0.662    0.024                      0.662    0.305

pj                1.444    0.066                      1.000    1.000

ij                1.576    0.057                      1.000    1.000

dj                1.466    0.060                      1.000    1.000