Latent Variable

(Updated 1/19/18--Previous updates 8/25/17, 5/10/16, 6/23/14, 5/17/13,      
1/23/13, 12/26/12, 2/6/12, 8/21/11, 6/09/10, 5/12/09,
4/3/09, 2/09/09, 6/12/08, 1/31/08, 10/26/07, 12/11/06)

Copyright (c) Robert Ping 2001-2018

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FOREWORD--This website contains research concerning the testing of theoretical models
 (hypothesis testing) using latent variables and real world survey data (with or without
 interactions or quadratics).
It is intended primarily for PhD students and researchers who are just getting started 
   with testing latent variable models using survey data. It contains, for example, 
suggestions for
reusing one's data for a second paper to help reduce "time
between papers." It also contains suggestions for
finding a consistent, valid and
reliable set of items (i.e., a set of items that fit the data), how to specify latent
variables with only 1 or 2 indicators, how to improve Average Variance Extracted,
a monograph on estimating latent variables, and selected papers.


A paper about reusing a data set to create a second theory-test paper is available
to help reduce the "time between papers"). It turns out that an editor might
not object to a paper that reuses data which has been used in a previously
published paper, if the new paper's theory/model is "interesting" and materially
different from
the previously published paper. The paper on reusing data discusses
how submodels from a previous paper might be found for a seco
nd paper that may
not require collecting new data.
(Please click here for more.)

Recent Additions and Changes (indicated by "New," "Revised" or "Updated"):

 o Comments on specifying and estimating a manifest (i.e., observed, single- indicator, etc.) variable as a latent variable, o suggestions for specifying and estimating a latent variable with only 2 indicators, o comments on the use
of regression in theoretical model (hypothesis) testing. o an EXCEL template to "weed" a measure so it "fits the data" (i.e., so it is internally consistent) and o several papers have been added, including one titled "What is Structural Equation Analysis?" that may be useful to those who would like to quickly gain a sense of this topic. o Some of the material below is duplicated elsewhere on the web sire (click here to
view the entire web site).
Please note: If you have visited this web site before, and the latest "Updated" 
date (at the top of the page) seems old, you may want to click on your browser's "Refresh" or "Reload" button on the browser toolbar (above) to view the current version of this web page.

All the material on this web site is copyrighted, but you may save it and print it 
   out. My only request is that you please cite any material that is helpful to you. APA 
   citations for the material below are shown with the material.
Don't forget to Refresh: Many of the links on this web site are in Microsoft WORD.
   If you have viewed one or more of them before, the procedure to view the latest
   (refreshed) version of them is tedious ("Refresh" does not work for Word documents
   on the web). With my apologies for the tediousness, to refresh any (and all) Word
   documents, please click on "Tools" on the browser toolbar (above), then click on
   "Internet Options...." Next, in the "General" tab, find the "Temporary Internet Files"
   section and click on "Delete Files...." Then, click in the "Delete all offline content" box,
   and click "OK." After that, close this browser window, then re-launch it so the latest
   versions of all the WORD documents are forced to download.
Your questions and comments are encouraged; just send an e-mail to 

Latent Variables:



Frequently Asked Question:
"Is there any way to speed up the process of attaining internal 
   consistency for a measure (making a multi-item measure fit the 
   data with more than 3 items)?" (Please see the first EXCEL
   template below.)

"What is structural equation analysis?"
    (Please click here for a paper on this matter, then please e-mail 
   me with any questions or comments you may have.)

"Why are reviewers complaining about my use of standardized loadings?"
   It turns out that standardized loadings (latent variable (LV) loadings specified
   as all free so the resulting LV has a variance of unity) may produce incorrect
   t-values for some parameter estimates, including structural coefficients. This
   presents a problem for theory testing: An incorrect (biased)
t-value for a
structural coefficient means that any interpretation of the structural
   coefficient's significance or nonsignificance versus its hypothesis may be risky.

     (Please click here for more.)

"Why are reviewers complaining about the use of multiple regression 
   in my paper?" (Please click here for a paper on this subject.)
"Is there any way to improve Average Variance Extracted (AVE) in a 
   Latent Variable X?"
    (Please click here for a paper on this matter.)

"How does one specify and estimate latent variables with only 1 or 2 
   (Please click here for a paper on this matter, then please consider
   e-mailing me--I have
more suggestions.)


EXCEL Templates:

For Latent Variable Regression, a measurement-error-adjusted regression approach to Structural Equation Analysis, for situations where regression
is useful (e.g., to estimate nominal/categorical variables with LV's) (see
Ping 1996, Multiv. Behav. Res., a revised version appears below).
More about the template.

For "weeding" a multi-item measure so it "fits the data" (i.e., finding 
   a set of items that "fits the data," so the measure is internally 
Note: In real-world data, there frequently are multiple subsets of a 
   multi-item measure that will "fit the data," and this raises the issue 
   of which of these subsets is "best" from a validity standpoint. This 
   template helps find at least one subset of items, usually with a 
maximal number of items (typically different from the one found
by maximizing reliability, and, so far, containing more than 3 items),
that will "fit the data." The template then can be used to search
for additional subsets of items that will also fit the data, and thus
it helps find the "best" face- or content valid subset of items in a measure. More about the template.

On-Line Monograph: 


The results of a large study of theoretical model (hypothesis) testing 
   practices using survey data, with critical analyses, suggestions and 
   examples. Potentially of interest to Ph.D. students and researchers 
   who conduct or teach theoretical model testing using survey data. 
   Contents include the six steps in theoretical model (hypothesis) 
   testing using survey data; Scenario Analysis; alternatives to 
   dropping items to attain model-to-data fit; inadmissible solutions 
   with remedies; interactions and quadratics; and pedagogical 
   examples (177 pp.).

Of particular interest lately is how to efficiently and effectively "weed" items to 
   attain a consistent measure (see STEP V, PROCEDURES FOR ATTAINING...).
The APA citation for this on-line monograph is Ping, R.A. (2004). Testing latent 
   variable models with survey data, 2nd edition. [on-line monograph]. 
   http://www.wright.edu/~robert.ping/lv1/toc1.htm .

(Edition 1)

Selected Papers on Latent Variables:


"On the Maximum of About Six Indicators per Latent Variable with 
   Real-World Data." (An earlier version of Ping 2008, Am. Mktng. 
   Assoc. (Winter) Educators� Conf. Proc.).

The paper suggests an explanation and remedies for the puzzling result that 
   Latent Variables in theoretical model testing articles all have a maximum of 
   about 6 indicators. 

"On Assuring Valid Measures for Theoretical Models Using Survey 
   Data" (An earlier version of Ping 2004, J. of Bus. Res., revised 
   December 2006).

The paper reviews and comments on extant procedures for creating valid 
   and reliable latent variable measures.

"But what about Categorical (Nominal) Variables in Latent Variable Models?"
(An earlier version of Ping 2009, Am. Mktng. Assoc. (Summer) Educators'
Conf. Proc.

In part because categorical variables almost always are measured in surveys in the
Social Sciences (e.g.,
"Demographics"), the paper suggests a procedure for estimating
nominal ("truly" categorical) variables in a structural equation model that also contains
 latent variables.


Copyright (c) Robert Ping 2006-2018