Creating a Rasch Model with GSS data

[Rachel Jones]

Hi all,

I'm trying to create a Rasch Model with GSS data and running into all sorts of issues. I've been following this Stata.com example (http://www.stata.com/support/faqs/st...s/rasch-model/) and it seems pretty helpful, but GSS data is not in the same format. The example requires data to be in the long format via the reshape command, but I'm unsure how to make my data fit that structure. I would be using the ID variable, the abortion variables, and the person's response for the particular abortion variable (yes/no). It would look something like this:
ID#1, abany, response
ID#1, abnomore, response
ID#1, absingle, response
ID#1, abpoor, response
ID#1, abdefect, response
ID#1, abrape, response
ID#1, abhlt, response
ID#2, abany, response
ID#2, abnomore, response
.....


So how I could I get my data to fit this structure so I could advance on with the Rasch model? The example uses this code below, but I'm unsure how "item" could reflect the person's individual response for the abortion variable.

reshape long math, i(subj_id) j(item)

I'm guessing I'd need to do something like this, but again, how I can I match up the response with the person's ID?

reshape long allabortionvariables, i(ID) j(response)

Below is the GSS code for the variables I'm interested in if that is helpful.

THANK YOU




. tab abany

ABORTION IF |
WOMAN WANTS |
FOR ANY |
REASON | Freq. Percent Cum.
------------+-----------------------------------
1 | 547 36.93 36.93
no | 934 63.07 100.00
------------+-----------------------------------
Total | 1,481 100.00

. tab abdefect

STRONG |
CHANCE OF |
SERIOUS |
DEFECT | Freq. Percent Cum.
------------+-----------------------------------
1 | 1,167 78.53 78.53
no | 319 21.47 100.00
------------+-----------------------------------
Total | 1,486 100.00

. tab abhlth

WOMANS |
HEALTH |
SERIOUSLY |
ENDANGERED | Freq. Percent Cum.
------------+-----------------------------------
1 | 1,332 89.34 89.34
no | 159 10.66 100.00
------------+-----------------------------------
Total | 1,491 100.00

. tab abnomore

MARRIED--WA |
NTS NO MORE |
CHILDREN | Freq. Percent Cum.
------------+-----------------------------------
1 | 600 40.32 40.32
no | 888 59.68 100.00
------------+-----------------------------------
Total | 1,488 100.00

. tab abpoor

LOW |
INCOME--CAN |
T AFFORD |
MORE |
CHILDREN | Freq. Percent Cum.
------------+-----------------------------------
1 | 650 43.68 43.68
no | 838 56.32 100.00
------------+-----------------------------------
Total | 1,488 100.00

. tab abrape

PREGNANT AS |
RESULT OF |
RAPE | Freq. Percent Cum.
------------+-----------------------------------
1 | 1,197 81.21 81.21
no | 277 18.79 100.00
------------+-----------------------------------
Total | 1,474 100.00

. tab absingle

NOT MARRIED | Freq. Percent Cum.
------------+-----------------------------------
1 | 612 41.18 41.18
no | 874 58.82 100.00
------------+-----------------------------------
Total | 1,486 100.00

[Clyde Schechter]

I think you want

reshape long ab*, i(subj_id) j(_item) string
encode _item, gen(item)
rename ab response

Notes:
1. This assumes that there are no other variables in your data set whose names begin with ab. If there are, some renaming or dropping of other variables is in order so that you can easily identify the questions you need using a wildcard.

2. I'm assuming that the Rasch model analysis will require you to have item numbers. The -reshape- by itself will have created a string variable, _item_ whose content is the original ab* variable name with "ab" stripped off. By -encoding- that you get a new numeric variable item with value labels that make it easy to use.

3. It's a little disturbing to see a variable which, when tabulated, has values 1 and no. Your response variable needs to be numeric. Are your ab* variables string variables, or are they numeric variables that are poorly labeled? If they are string variables, you need to follow up the code shown above with something like

replace response = trim(itrim(response))
replace response = "0" if response == "no"
destring response, replace

If they are numeric variables, I would instead run the following double-check:

assert inlist(response, 0, 1) if !missing(response)

For future reference, my response could have been shorter, and clearer, with fewer ramifications for contingencies about unknown aspects of the data, had you posted some example data using the -dataex- command. (If you don't have -dataex-, run -ssc install dataex- and then read -help dataex- for the simple instructions on how to use it.) That way, anyone interested in responding could quickly, easily, and faithfully replicate that sample of your data and write a response that deals with your data as it is, rather than a branching response that deals with several possibilities of what your data might be.

[wbuchanan]

Reshaping the data is not necessary if you are using the most current version of Stata. The IRT commands don't allow user specified parameter constraints, but you can use raschjmle to fit a Rasch model without having to modify the data structure (assuming you have one observation per subject and the variables contain the responses. If you're fine with using a 1PL model you can fit it with

irt 1pl varlist

If you are using the xtlogit/cloglog approaches, once you've restructured your data you need to create the design matrix:

qui: levelsof item, loc(x)
foreach v of loc x {
qui: g byte `v' = item == `"`x'"'
}

This would give you the identity matrix for the response set. This would also be the format you would want to use if you were fitting the model with gllamm.

[ben earnhart]

Just for the sake of my own selfish wondering, I have uploaded the data she wants to use. Given the actual dataset and such, how would one model it? I'm inclined to do a CFA with gsem, because I'm relatively ignorant of IRT. But a CFA blind is no good...

[wbuchanan]

ben earnhart I think you've managed to hit a bigger issue than previously discussed. With the exception of using gllamm or the bayesmh commands, all of the IRT capabilities available in Stata are based on the data conforming to a strictly unidimensional model. So, in order to fit the CFA and/or Rasch model, there is an implicit assumption that the latent structure of those data are known. A bigger issue in this particular case is the nature of the collected data. When the data are longitudinal in nature, it become necessary to verify that the items are invariant over time (e.g., measure the same thing the same way each year) so any differences in latent means/variance (as an example) can be attributed to true changes in the underlying latent construct and not a change in how people interpret the items. Within the CTT tradition, this would be accomplished using a multigroup CFA where a base line model would be fitted and different constraints would be added/modified to test different types of measurement invariance over time. In the IRT tradition, once the items are calibrated (and assuming the item stems are constant over time) the forms would be linked/equated using anchoring items and/or other linking/equating designs/models.

I'm not sure how well these data fit a unidimensional model:

use ~/Downloads/abexample.dta, clear
rename *, lower
drop if mi(caseid)
la def bin 0 "No" 1 "Yes"
foreach v of var abany abnomore absingle abpoor abdefect abrape abhlth {
    qui: replace `v' = cond(`v' == 2, 0, `v')
    la val `v' bin
}
gsem (Support -> abany abnomore absingle abpoor abdefect abrape abhlth)      ///   
if year == 2006, logit

I let the model run until it hit the 41st iteration, but the model wouldn't converge. I used the 2006 sample because there were a larger number of observations, but it definitely struck me as odd that it would take that long to converge.

[ben earnhart]

There do appear to be two factors:

. polychoric ab* if year==2006

Polychoric correlation matrix

              abany   abnomore   absingle     abpoor   abdefect     abrape     abhlth
   abany          1
abnomore  .95205234          1
absingle  .96429963  .96502806          1
  abpoor  .93349292  .95164608  .96101494          1
abdefect  .79502601  .85178611  .88534184  .86707354          1
  abrape  .79808533   .7813683  .83011396  .84844744  .86034744          1
  abhlth  .74150892  .78530248  .79033992  .82863035  .87859628  .85493812          1

. 
. global N = r(sum_w)

. 
. matrix r = r(R)

. factormat r, n($N)
(obs=1,764)

Factor analysis/correlation                      Number of obs    =      1,764
    Method: principal factors                    Retained factors =          4
    Rotation: (unrotated)                        Number of params =         21

    --------------------------------------------------------------------------
         Factor  |   Eigenvalue   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      6.10692      5.77334            0.9491       0.9491
        Factor2  |      0.33358      0.28355            0.0518       1.0009
        Factor3  |      0.05003      0.03145            0.0078       1.0087
        Factor4  |      0.01858      0.02102            0.0029       1.0116
        Factor5  |     -0.00244      0.03050           -0.0004       1.0112
        Factor6  |     -0.03294      0.00633           -0.0051       1.0061
        Factor7  |     -0.03927            .           -0.0061       1.0000
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(21) = 2.4e+04 Prob>chi2 = 0.0000

Factor loadings (pattern matrix) and unique variances

    ---------------------------------------------------------------------
        Variable |  Factor1   Factor2   Factor3   Factor4 |   Uniqueness 
    -------------+----------------------------------------+--------------
           abany |   0.9422   -0.2627    0.0951   -0.0235 |      0.0336  
        abnomore |   0.9569   -0.1967   -0.0815    0.0623 |      0.0352  
        absingle |   0.9770   -0.1610   -0.0460   -0.0751 |      0.0118  
          abpoor |   0.9707   -0.0831    0.0279    0.0585 |      0.0466  
        abdefect |   0.9250    0.2275   -0.1260   -0.0412 |      0.0750  
          abrape |   0.8884    0.2271    0.1239   -0.0298 |      0.1430  
          abhlth |   0.8729    0.2995    0.0147    0.0500 |      0.1456  
    ---------------------------------------------------------------------

. 
. 
. factormat r, n($N) factors(2)
(obs=1,764)

Factor analysis/correlation                      Number of obs    =      1,764
    Method: principal factors                    Retained factors =          2
    Rotation: (unrotated)                        Number of params =         13

    --------------------------------------------------------------------------
         Factor  |   Eigenvalue   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      6.10692      5.77334            0.9491       0.9491
        Factor2  |      0.33358      0.28355            0.0518       1.0009
        Factor3  |      0.05003      0.03145            0.0078       1.0087
        Factor4  |      0.01858      0.02102            0.0029       1.0116
        Factor5  |     -0.00244      0.03050           -0.0004       1.0112
        Factor6  |     -0.03294      0.00633           -0.0051       1.0061
        Factor7  |     -0.03927            .           -0.0061       1.0000
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(21) = 2.4e+04 Prob>chi2 = 0.0000

Factor loadings (pattern matrix) and unique variances

    -------------------------------------------------
        Variable |  Factor1   Factor2 |   Uniqueness 
    -------------+--------------------+--------------
           abany |   0.9422   -0.2627 |      0.0432  
        abnomore |   0.9569   -0.1967 |      0.0457  
        absingle |   0.9770   -0.1610 |      0.0196  
          abpoor |   0.9707   -0.0831 |      0.0508  
        abdefect |   0.9250    0.2275 |      0.0926  
          abrape |   0.8884    0.2271 |      0.1593  
          abhlth |   0.8729    0.2995 |      0.1483  
    -------------------------------------------------

. rotate, promax

Factor analysis/correlation                      Number of obs    =      1,764
    Method: principal factors                    Retained factors =          2
    Rotation: oblique promax (Kaiser off)        Number of params =         13

    --------------------------------------------------------------------------
         Factor  |     Variance   Proportion    Rotated factors are correlated
    -------------+------------------------------------------------------------
        Factor1  |      5.52188       0.8582
        Factor2  |      5.18070       0.8051
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(21) = 2.4e+04 Prob>chi2 = 0.0000

Rotated factor loadings (pattern matrix) and unique variances

    -------------------------------------------------
        Variable |  Factor1   Factor2 |   Uniqueness 
    -------------+--------------------+--------------
           abany |   0.9207    0.0758 |      0.0432  
        abnomore |   0.8393    0.1760 |      0.0457  
        absingle |   0.8026    0.2359 |      0.0196  
          abpoor |   0.6925    0.3430 |      0.0508  
        abdefect |   0.2413    0.7599 |      0.0926  
          abrape |   0.2201    0.7418 |      0.1593  
          abhlth |   0.1120    0.8368 |      0.1483  
    -------------------------------------------------

Factor rotation matrix

    --------------------------------
                 | Factor1  Factor2 
    -------------+------------------
         Factor1 |  0.9480   0.9163 
         Factor2 | -0.3183   0.4005 
    --------------------------------

[wbuchanan]

One problem is likely going to be the sparsity of some of the cell sizes:

. tab2 ab* if year == 2006

-> tabulation of abany by abnomore if year == 2006 

  ABORTION |
  IF WOMAN |   MARRIED--WANTS NO
 WANTS FOR |     MORE CHILDREN
ANY REASON |        No        Yes |     Total
-----------+----------------------+----------
        No |     1,016        112 |     1,128 
       Yes |        77        698 |       775 
-----------+----------------------+----------
     Total |     1,093        810 |     1,903 


-> tabulation of abany by absingle if year == 2006 

  ABORTION |
  IF WOMAN |
 WANTS FOR |      NOT MARRIED
ANY REASON |        No        Yes |     Total
-----------+----------------------+----------
        No |     1,063         79 |     1,142 
       Yes |        83        692 |       775 
-----------+----------------------+----------
     Total |     1,146        771 |     1,917 


-> tabulation of abany by abpoor if year == 2006 

  ABORTION |
  IF WOMAN |   LOW INCOME--CANT
 WANTS FOR | AFFORD MORE CHILDREN
ANY REASON |        No        Yes |     Total
-----------+----------------------+----------
        No |       996        132 |     1,128 
       Yes |        93        683 |       776 
-----------+----------------------+----------
     Total |     1,089        815 |     1,904 


-> tabulation of abany by abdefect if year == 2006 

  ABORTION |
  IF WOMAN |   STRONG CHANCE OF
 WANTS FOR |    SERIOUS DEFECT
ANY REASON |        No        Yes |     Total
-----------+----------------------+----------
        No |       468        641 |     1,109 
       Yes |        22        754 |       776 
-----------+----------------------+----------
     Total |       490      1,395 |     1,885 


-> tabulation of abany by abrape if year == 2006 

  ABORTION |
  IF WOMAN | PREGNANT AS RESULT OF
 WANTS FOR |         RAPE
ANY REASON |        No        Yes |     Total
-----------+----------------------+----------
        No |       412        690 |     1,102 
       Yes |        16        765 |       781 
-----------+----------------------+----------
     Total |       428      1,455 |     1,883 


-> tabulation of abany by abhlth if year == 2006 

  ABORTION |
  IF WOMAN |     WOMANS HEALTH
 WANTS FOR | SERIOUSLY ENDANGERED
ANY REASON |        No        Yes |     Total
-----------+----------------------+----------
        No |       225        883 |     1,108 
       Yes |         7        775 |       782 
-----------+----------------------+----------
     Total |       232      1,658 |     1,890 


-> tabulation of abnomore by absingle if year == 2006 

MARRIED--W |
   ANTS NO |
      MORE |      NOT MARRIED
  CHILDREN |        No        Yes |     Total
-----------+----------------------+----------
        No |     1,032         61 |     1,093 
       Yes |       102        703 |       805 
-----------+----------------------+----------
     Total |     1,134        764 |     1,898 


-> tabulation of abnomore by abpoor if year == 2006 

MARRIED--W |
   ANTS NO |   LOW INCOME--CANT
      MORE | AFFORD MORE CHILDREN
  CHILDREN |        No        Yes |     Total
-----------+----------------------+----------
        No |       995         95 |     1,090 
       Yes |        94        713 |       807 
-----------+----------------------+----------
     Total |     1,089        808 |     1,897 


-> tabulation of abnomore by abdefect if year == 2006 

MARRIED--W |
   ANTS NO |   STRONG CHANCE OF
      MORE |    SERIOUS DEFECT
  CHILDREN |        No        Yes |     Total
-----------+----------------------+----------
        No |       480        586 |     1,066 
       Yes |        15        796 |       811 
-----------+----------------------+----------
     Total |       495      1,382 |     1,877 


-> tabulation of abnomore by abrape if year == 2006 

MARRIED--W |
   ANTS NO | PREGNANT AS RESULT OF
      MORE |         RAPE
  CHILDREN |        No        Yes |     Total
-----------+----------------------+----------
        No |       406        643 |     1,049 
       Yes |        20        793 |       813 
-----------+----------------------+----------
     Total |       426      1,436 |     1,862 


-> tabulation of abnomore by abhlth if year == 2006 

MARRIED--W |
   ANTS NO |     WOMANS HEALTH
      MORE | SERIOUSLY ENDANGERED
  CHILDREN |        No        Yes |     Total
-----------+----------------------+----------
        No |       228        832 |     1,060 
       Yes |         4        813 |       817 
-----------+----------------------+----------
     Total |       232      1,645 |     1,877 


-> tabulation of absingle by abpoor if year == 2006 

           |   LOW INCOME--CANT
       NOT | AFFORD MORE CHILDREN
   MARRIED |        No        Yes |     Total
-----------+----------------------+----------
        No |     1,028        111 |     1,139 
       Yes |        60        702 |       762 
-----------+----------------------+----------
     Total |     1,088        813 |     1,901 


-> tabulation of absingle by abdefect if year == 2006 

           |   STRONG CHANCE OF
       NOT |    SERIOUS DEFECT
   MARRIED |        No        Yes |     Total
-----------+----------------------+----------
        No |       481        627 |     1,108 
       Yes |         8        764 |       772 
-----------+----------------------+----------
     Total |       489      1,391 |     1,880 


-> tabulation of absingle by abrape if year == 2006 

           | PREGNANT AS RESULT OF
       NOT |         RAPE
   MARRIED |        No        Yes |     Total
-----------+----------------------+----------
        No |       417        684 |     1,101 
       Yes |        12        765 |       777 
-----------+----------------------+----------
     Total |       429      1,449 |     1,878 


-> tabulation of absingle by abhlth if year == 2006 

           |     WOMANS HEALTH
       NOT | SERIOUSLY ENDANGERED
   MARRIED |        No        Yes |     Total
-----------+----------------------+----------
        No |       228        884 |     1,112 
       Yes |         4        773 |       777 
-----------+----------------------+----------
     Total |       232      1,657 |     1,889 


-> tabulation of abpoor by abdefect if year == 2006 

       LOW |
INCOME--CA |
 NT AFFORD |   STRONG CHANCE OF
      MORE |    SERIOUS DEFECT
  CHILDREN |        No        Yes |     Total
-----------+----------------------+----------
        No |       480        578 |     1,058 
       Yes |        12        805 |       817 
-----------+----------------------+----------
     Total |       492      1,383 |     1,875 


-> tabulation of abpoor by abrape if year == 2006 

       LOW |
INCOME--CA |
 NT AFFORD | PREGNANT AS RESULT OF
      MORE |         RAPE
  CHILDREN |        No        Yes |     Total
-----------+----------------------+----------
        No |       418        629 |     1,047 
       Yes |        10        810 |       820 
-----------+----------------------+----------
     Total |       428      1,439 |     1,867 


-> tabulation of abpoor by abhlth if year == 2006 

       LOW |
INCOME--CA |
 NT AFFORD |     WOMANS HEALTH
      MORE | SERIOUSLY ENDANGERED
  CHILDREN |        No        Yes |     Total
-----------+----------------------+----------
        No |       230        832 |     1,062 
       Yes |         2        818 |       820 
-----------+----------------------+----------
     Total |       232      1,650 |     1,882 


-> tabulation of abdefect by abrape if year == 2006 

    STRONG |
 CHANCE OF | PREGNANT AS RESULT OF
   SERIOUS |         RAPE
    DEFECT |        No        Yes |     Total
-----------+----------------------+----------
        No |       321        152 |       473 
       Yes |       100      1,297 |     1,397 
-----------+----------------------+----------
     Total |       421      1,449 |     1,870 


-> tabulation of abdefect by abhlth if year == 2006 

    STRONG |
 CHANCE OF |     WOMANS HEALTH
   SERIOUS | SERIOUSLY ENDANGERED
    DEFECT |        No        Yes |     Total
-----------+----------------------+----------
        No |       209        260 |       469 
       Yes |        21      1,390 |     1,411 
-----------+----------------------+----------
     Total |       230      1,650 |     1,880 


-> tabulation of abrape by abhlth if year == 2006 

  PREGNANT |     WOMANS HEALTH
 AS RESULT | SERIOUSLY ENDANGERED
   OF RAPE |        No        Yes |     Total
-----------+----------------------+----------
        No |       191        219 |       410 
       Yes |        35      1,430 |     1,465 
-----------+----------------------+----------
     Total |       226      1,649 |     1,875

Just trying to get a model to fit these data seems like a bit of a challenge. Does Rachel Jones know whether or not the survey was designed to measure a more generalized feelings/support for abortion type construct? In either case, it seems like there is a lot of work that needs to be done fitting any type of IRT models to the data.

[Rachel Jones]

Thank you all so much for your advice and input! I'm still so new to Stata so this is a bit overwhelming for me, but I am learning a lot!

Anyway, wbuchanan I don't believe the GSS was designed to create any sort of general abortion construct. The creators of the GSS ask the participants many questions and they change year to year without any theory behind it.

ben earnhart I know confirmatory factor analysis are not good without theory, but some of the literature I've read would suggest that the types of questions would actually break up into the two factors you have found.

I'm interested in finding any sort of structure that differentiates the more liberal attitudes (i.e. abortion for any reason) from the more conservative ones(i.e pregnant as result of rape). Would a factor analysis be sufficient to do this?

Thank you all again!

[wbuchanan]

Rachel Jones it sounds like you are having a scaling issue. Do you have any data available on the participants' political leanings? The problem with a CFA in this case is that the items aren't developed to measure the two different factors you've mentioned. If the item stems change over time that could affect the latent in a manner that is artificial. I tried letting a CFA run a few different times with the data and it seemed like there were some problems with convergence (e.g., model wouldn't converge, log likelihoods were decreasing in magnitude for several iterations then increasing, etc...). The other issue you'd be likely to face with a Rasch model is the number of items available given that the items weren't developed to measure the construct (e.g., reliability will suffer from the small number of items).

[ben earnhart]

Rachael --

I couldn't get logit-linked CFA on the 2006 data to converge, either, even with my cheating and using the EFA to inform me what the model should look like. A regular ML model (assuming normality) converged easily, but that isn't appropriate for dummy variables. I think you can tell by now that a Rasch model is not feasible, and even a CFA is probably not, either. But at least part of the problem is that the items covary so strongly -- if you look at the matrix from polychoric the smallest correlation was .74, and if you run alpha on the raw items, they all add to the alpha except maybe abhlth.

So if your goal was a nice methods paper, it's not good data for that, If you want to use the items as a scale, then using them as a single scale has some arguments for it, and separating them as per the EFA output has some arguments for it. BTW, when I run alpha on just the first four items, it gets a .93, which is absurdly high for four dummy variables. I guess you look to the literature and see how others have done it and why.

Do you have access to Mplus? It can do Exploratory SEM (which is an oxymoron to most people, but Muthen has published papers on it). With Mplus, you could do an EFA, taking into account the fact you're using dummy variables. That might be the best you could do.

[Rachel Jones]

I do have data on the participant's political leanings, but I was hoping to create some sort of abortion attitude scale that I can link to other variables.

I do not have access to Mplus (though I'm sure if I had to I could find it somewhere at my University).

Previously I was trying to do a summation scale, but do you think it would be acceptable to create a scale based on the two factors found in the EFA? (something that separates the variables into liberal vs conservative attitudes towards abortion)

Thank you both again so much!