POLS 6386 MEASUREMENT THEORY
Fourth Assignment
Due 28 February 2001


  1. The aim of this problem is to show you how to use metric unfolding to analyze thermometer scores. To do this you need to run a program that unfolds the thermometer scores. We are going to analyze the class 1968 feeling thermometers. Download the the program, control card file, and data file and place them in the same directory.

    Metric Unfolding Program (MLSMU6_2010.F95) -- Can easily be compiled with gfortran.

    unfold_1968.ctl -- Control Card File for Metric Unfolding Program

    1968 Election Data

    The 1968 Election Data file contains the same variables that we have used in the past plus the thermometer scores and voting information for the respondents. The variables are:
    
    idno           respondent id number
    partyid        strength of party id -- 0 to 6
    income         raw income category
    incomeq        income quintile -- 1 to 5
    race           0 = white, 1 = black
    sex            0 = man, 1 = woman
    south          0 = north, 1 = south
    education      1=HS, 2=SC, 3=College
    age            age in years
    uulbj          lbj position urban unrest
    uuhhh          humphrey pos urban unrest
    uunixon        nixon position urban unrest
    uuwallace      wallace pos urban unrest
    uuself         self placement urban unrest
    vnmlbj         lbj pos vietnam
    vnmhhh         hhh pos vietnam
    vnmnixon       nixon pos vietnam
    vnmwallace     wallace pos vietnam
    vnmself        self placement vietnam
    voted          1=voted, 5=did not vote
    votedfor       who voted for -- 1 = humphrey, 2= nixon, 3=wallace
    wallace        wallace therm
    humphrey       humphrey thermometer
    nixon          nixon thermometer
    mccarthy       mccarthy thermometer
    reagan         reagan thermometer
    rockefeller    rockefeller thermometer
    lbj            lbj thermometer
    romney         romney thermometer
    kennedy        robert kennedy thermometer
    muskie         muskie thermometer
    agnew          agnew thermometer
    lemay          "bombs away with Curtis LeMay" thermometer
    
    The control card file for the metric unfolding procedure is shown below. The first line has the name of the data file. The first number in the second line is the number of stimuli, the next two numbers are the minimum and maximum number of dimensions to estimate, and the "10" is the number of iterations.

    The third line contains some "antique" options we will never use. The only numbers that matter on this line are the "4" which indicates the number of identifying characters to read off each line of the data file (e.g., the respondent id number), and the "2" at the end. This is the number of missing data codes which appear in the sixth line.

    The first number in the fourth line is a tolerance value -- leave it as is. The next three numbers are parameters to transform the input data into squared distances. In this case, let amx=-.02, bmx=2.0, and cmx=2.0. The following equation transforms the thermometers into squared distances:

    d2 = (amx*t+bmx)cmx

    where t = input data. This formula takes a linear transformation of the input data to the power cmx. With amx = -.02, bmx = 2.0, and cmx = 2.0, this is equivalent to subtracting the thermometer score from 100, dividing by 50, and then squaring. This converts t from a 0-100 scale to a 4-0 scale. If the data, t, are distances, set amx = 1.0, bmx = 0.0, and cmx = 2.0. If the data are correlations, set amx = -1.0, bmx = 1.0, and cmx=2.0 or 1.0 if the correlations are initially regarded as unsquared or squared distances respectively.

    The next value, "1.5", is the maximum absolute expected coordinate value on any dimension. It is used for plotting purposes. If the squared distances are confined to a 4-0 scale, xmax=1.5 is usually sufficient. The last two numbers, "0.0" and "100.0", are the minimum and maximum expected values of the input data. These are used to catch coding errors in the input data. Anything out of range is treated as missing data.

    The fifth line is the format of the data file and the sixth line contains the missing data codes.

    Finally, the last 12 lines are labels for the stimuli.
    OLS68B.DAT
       12    2    2   10    0    0
        1    1    0    4    2
        .001  -0.02    2.0     2.0     1.5     0.0   100.0
    (1X,4A1,60X,12F3.0)
     98 99
    WALLACE
    HUMPHREY
    NIXON   
    MCCARTHY
    REAGAN
    ROCKEFELLER
    LBJ   
    ROMNEY 
    R.KENNEDY
    MUSKIE   
    AGNEW
    LEMAY   
    1. Put OLS68B.DAT into Excel and compute the correlation matrix between the 12 sets of candidate feeling thermometers. Turn in the correlation matrix (note that the correlation matrix will not be entirely accurate because of the missing data codes, 98 and 99!).

    2. Put OLS68B.DAT into Stata and define the variables appropriately.

    3. Run MLSMU6. It will produce an output file called FORT.22. The first 20 lines look like this:
      
       WALLACE          1.2646    0.5154  217.4823    0.5541 1242.0000
       HUMPHREY        -0.5559    0.3738  114.7892    0.6968 1252.0000
       NIXON            0.1480   -0.5415  123.2209    0.5319 1250.0000
       MCCARTHY        -0.6251   -0.4938  151.8926    0.3854 1204.0000
       REAGAN           0.3080   -0.8895  131.8091    0.4380 1212.0000
       ROCKEFELLER     -0.5579   -0.5995  148.1413    0.3724 1229.0000
       LBJ             -0.5223    0.4905  147.0334    0.5573 1253.0000
       ROMNEY          -0.4736   -0.7866  111.3147    0.3434 1167.0000
       R.KENNEDY       -0.4245    0.2351  148.8571    0.5418 1242.0000
       MUSKIE          -0.6611    0.1660  126.0836    0.4862 1177.0000
       AGNEW            0.2341   -0.8706  114.1418    0.4675 1180.0000
       LEMAY            1.1901    0.4267  174.3242    0.4601 1188.0000
       1681            -0.0285    0.2555    0.7918    0.6824   12.0000
       1124            -0.1768    0.2692    1.4788    0.6992   12.0000
         78             0.5707   -0.1514    3.5611    0.2141   12.0000
        553             0.1376    0.1064    0.1597    0.7047    9.0000
          7             0.2542    0.1235    1.2634    0.0116   12.0000
        412             0.2781    0.0867    0.1024    0.6197   12.0000
        631             0.5017    0.1088    1.1196    0.0742   12.0000
       1316             0.2175   -0.5842    1.1568    0.8577   12.0000
      The first two columns after the names are the two dimensional coordinates. The first 12 lines are the coordinates for the political candidates and lines 13 onward are the coordinates for the respondents. Use SPSS to plot the 12 candidates in two dimensions.

    4. Merge the two dimensional coordinates of the respondents into your Stata file. Turn in the results of the d and summ commands. Be sure that you have defined everything properly!

    5. Create three new variables -- the squared distances from each respondent to Wallace, Humphrey, and Nixon. Turn in the summ command for these variables.

    6. Use Probit and Logit to test the following models:

      Voted For Humphrey = f(partyid, income quintile, race, sex, south, education, age, squared distance to Wallace, squared distance to Humphrey, squared distance to Nixon)

      Voted For Nixon = f(partyid, income quintile, race, sex, south, education, age, squared distance to Wallace, squared distance to Humphrey, squared distance to Nixon)

      Voted For Wallace = f(partyid, income quintile, race, sex, south, education, age, squared distance to Wallace, squared distance to Humphrey, squared distance to Nixon)

      The dependent variables are "1" if the respondent voted and voted for Humphrey/Nixon/Wallace respectively, and "0" otherwise.

      What should the signs be on the independent variables? Why?

    7. Run the specifications in part (f) using only for those respondents who actually voted (if voted==1).

    8. Paste the dataset into EVIEWS and replicate the probits and logits.