Have you considered IRT? The output is often useful for examining the relationships between the dichotomous items and whichever latent traits you have. A package often used, in R, is mirt (https://cran.r-project.org/web/packages/mirt/mirt.pdf). But if you just want polychoric correlations, see (http://127.0.0.1:28397/library/polycor/html/polychor.html).

YES! Urbano Lorenzo-Seva has a free program exactly for this. I've used it extensively and it works quite well. There is a bit of a steep learning curve if you are new to these topics, but it's free and once you get the hang of it, it is quite good. No coding involved (like R), and it's relatively user-friendly. I have no connection it, but I'm a fan.

https://psico.fcep.urv.cat/utilitats/factor/

Mplus does both binary/ordinal factor analysis based on tetrachoric/polychoric correlations and item response theory (IRT) models.

You could try the SPSSINC HETCOR extension command. I've pasted the help file below. See this YouTube video for info on how to find and install extension commands:

• https://www.youtube.com/watch?v=0vB-VfnT3ok

SPSSINC HETCOR Extension Command

Compute a set of Pearson, polychoric, or polyserial correlations according the measurement levels of the variables.

SPSSINC HETCOR variables*

/OPTIONS ESTIMATOR=TWOSTEP** or ML STDERR=TRUE** or FALSE N=TRUE** or FALSE TYPE=TRUE** or FALSE MISSING=PAIRWISE** or LISTWISE EXECUTE=TRUE** or FALSE

/SAVE PROGRAMFILE=“filespec”

* Required ** Default

SPSSINC HETCOR /HELP prints this information and does nothing else.

Split files and weight are not honored by this command.

SPSSINC HETCOR var1 var2 var3 /OPTIONS STDERR=TRUE.

The variable list specifies the variables to be correlated. The type of correlation is determined by the measurement levels of each pair of variables.

OPTIONS

ESTIMATOR specifies the estimator. TWOSTEP may execute considerably faster and is the default. ML can fail to converge in some cases.

STDERR=TRUE causes a standard error to be included in the output.

N=TRUE causes the count for each correlation to be displayed. It is ignored if STDERR=FALSE.

TYPE=TRUE causes a separate table of the correlation types to be displayed.

EXECUTE=FALSE processes the command syntax but does not execute it. This is mainly useful in combination with SAVE PROGRAMFILE.

PROGRAMFILE

PROGRAMFILE causes the R code that implements the hetcor function to be written to the specified file.

The SPSSINC HETCOR command requires both the Python and R Integration Plug-ins. package.

© Copyright IBM Corp. 1989, 2014