One of the many cool things about Mplus is that you have the option to run individual and summary data. And what does that mean exactly? Well, in addition to the typical individual data where each tab separated colum is a variable (like you’d see in a typical dataset), like this:
…you can take a correlation table (along with the means, standard deviations, and sample size) like this:
…and run analyses like you normally would. Now, that’s pretty cool.
What you see in the summary data file is
first line: means
second line: standard deviations
third line onwards: lower diagonal of your correlation/covariance matrix
and all else you would need to do is specify a few more things under the DATA command line to run analysis like normal:
Type = means stdeviations correlations;
Nobservations = # of observations in dataset;
and this would look like the following:
On another note, if you have a full correlation or covariance matrix instead of only the bottom diagonal, you would replace correlation in the Type subcommand with FULLCORR or FULLCOV
Otherwise have at it the same way you would typically run analyses with individual level data — but now you also have a tool to check the integrity of published analyses!
Hofmann & Morgeson (1999) example
When I heard about the ability to use summary data, I thought it was incredibly cool but never actually tried it out for myself (beyond using a dataset that was already prepared with summary data). So I went and tried it out for myself and here are the steps I took:
Locate an article that has a correlation table, means, standard deviations and sample size available. In my case, I just picked a random article on support and employee safety from a top journal in my field (Hofmann & Morgeson, 1999).
Record data into a .dat file (at least 2 easy options)
- [Easiest] On Mac, open TextEdit (for Windows, it is probably similar with Notepad) and make sure it is in Plain text (to check, go to Format and look for “Make Plain Text”, if it is already in this format, you will see Make Rich Text)
- Enter the means on the top row: start tight to top left corner, enter a number, press tab, enter next number, etc.
- Enter standard deviations on second row: press enter once all means are in, and repeat the same thing with standard deviations making sure they are separated by pressing tab
- Enter correlation/covariance table the same way you entered the means and standard deviations
- Save file with the extension: .dat
- [Second easiest] Do the same thing in SPSS
- Save as Fixed ASCII (*.dat)
Write your syntax and save it in the same folder as the data file. Below is an example of the syntax as a screenshot and a copy-and-paste ready code
TITLE: Sample summary data analysis on Hofmann & Morgeson 1999; DATA: File is H&M1999.dat; Type is MEANS STDEVIATIONS CORRELATION; Nobservations = 49; !they have uneven observations by variable, but we'll stick with 49 VARIABLE: names are POS LMX SCMU SCMI ACC AGE ORGT JOBT; !POS = perceived org support !LMX = leader-member exchange !SCMU = safety communication !SCMI = safety commitment !ACC = accidents !ORGT = org tenure !JOBT = job tenure usevariables = POS LMX SCMU SCMI ACC; !H1&2: POS & LMX +r w/ SCMU !H3&4: POS & LMX +r w/ SCMI !H5: SCMU +r w/ SCMI !H6&7: SCMU & SCMI -r w/ ACC ANALYSIS: Estimator = ML; MODEL: SCMU on POS LMX; !H1&2 SCMI on POS LMX; !H3&4 SCMU with SCMI; !H5 ACC on SCMU SCMI; !H6&7 OUTPUT: Standardized sampstat TECH1;
Press run and see if it works! Below is the output that was produced when I ran the above syntax. The results of interest can be found under STANDARDIZED MODEL RESULTS. We can see that we replicate the basic findings for hypotheses 1-5 (a non-finding in the case of hypothesis 3), but we actually do not find that safety communication and safety commitment have a significant negative association with accidents (likely due to power issues in how I ran the analyses – they only looked at the correlation coefficients, while I ran a multiple regression which takes into account overlapping variance):
I also ran their structural model over again with indirect affects for anyone who is interested. Because I did not correct for their small sample size (and to be frank, I’m not entirely familiar with the strategy they took), the model fit is rather less than satisfactory (χ²(5) = 7.43, p = .19, CFI = .92, TLI = .85, RMSEA = .10, and SRMR = .08) and the path coefficients are somewhat smaller (click to expand and view output):
However, if you run the additional analyses they ran (controlling for organizational tenure), the model fit improves substantially (χ²(5) = 10.02, p = .35, CFI = .97, TLI = .96, RMSEA = .05, and SRMR = .09) but the relationship between safety commitment and accidents is no longer significant (again, likely an issue with power due to small sample size):
In any case, this is the kind of stuff you can do with Mplus! Enjoy!
Hofmann, D. A., & Morgeson, F. P. (1999). Safety-related behavior as a social exchange: The role of perceived organizational support and leader–member exchange. Journal of applied psychology, 84(2), 286-296.