Analyzing electoral utilities by way of a stacked data-matrix

1. January 6-9, 2005 EES2004 Data Confrontation Seminar University of Nottingham 1 Analyzing electoral utilities by way of a stacked data-matrix Cees van der Eijk (University of Nottingham) cees.vandereijk@nottingham.ac.uk

2. 6-9 January 2005 Data Confrontation SeminarNottingham 2 Analyzing electoral utilities The philosophy of analyzing party choice via electoral utilities has been described in detail elsewhere: Tillie 1995 van der Eijk & Franklin 1996 (Ch. 20) van der Eijk et al. 2005 The procedure described in this document is geared towards SPSS. Stacking in STATA is somewhat easier, but there, too, the construction of independent variables requires separate attention

3. 6-9 January 2005 Data Confrontation SeminarNottingham 3 Constructing a stacked data-file for every respondent the same question has been asked for each of a set of parties (e.g., electoral utilities), each of these is a separate variable (column) in the data-matrix. These separate variables are to be stacked in order to analyze them as a single dependent variable Stacking involves the transformation of a file where records are respondents into a file where the records are respondent* party combinations Analyzing the stacked dependent variable requires the independent variables to be also defined in respondent*party terms, and to be stacked as well

4. 6-9 January 2005 Data Confrontation SeminarNottingham 4 Constructing a �stacked� datafile If the data pertain to various countries (as is the case in EES data) the following procedure has to be performed for each country separately. If one would like to analyze the data from all countries simultaneously, this can be done by pooling the stacked data-files of the various countries (in SPSS by merge files>add cases) The procedure has to be performed simultaneously for all dependent and independent variables. If one wants to add another independent in a later stage, the process has to be started all over again

5. 6-9 January 2005 Data Confrontation SeminarNottingham 5 Sequence of steps Identify dependent and independent variables. The dependent variable usually does not require any special treatment before stacking Insert in the unstructured dataset a set of variables for the identification of the stacks (i.e., in our case: parties) If necessary: transform the independent variables into an appropriate form Use the Restructure option in the SPSS data menu for the actual stacking

6. 6-9 January 2005 Data Confrontation SeminarNottingham 6 Identification of stacks Create as many identifying variables as there are parties. These variables have the same value for each respondent in the unstructured data-file (they are thus constants). In the case of, e.g., 6 parties: compute p1=1. compute p2=2. compute p3=3. compute p4=4. compute p5=5. compute p6=6. These variables will also be stacked, in order to yield a single identifier for parties in the stacked file. In the restructuring procedure in SPSS this stacked variable can be named at will.

7. 6-9 January 2005 Data Confrontation SeminarNottingham 7 Transformation of independents Independent variables in the stacked file should (often) be of a nature that they pertain to a respondent*party combination. In other words: they should reflect a relationship between a voter and a party. This can be done in different ways: Distances i.e. between voter and each of the parties on the L/R scale, pro/anti EU scale (NB: define distances by absolute differences!) Theoretically constructed similarities, entirely to be justified in theoretical terms and contextual knowledge of the party system in question. For example, if religion is an important cleavage: voter is religious AND party is religious: similarity=1 voter is not religious AND party is not religious: similarity=1 voter is not religious AND party is religious: similarity=0 voter is religious AND party is not religious: similarity=0 Inductively generated independent variables pertaining to voter*party combinations (works always): Y-hat procedure (see next sheet)

8. 6-9 January 2005 Data Confrontation SeminarNottingham 8 Y-hat procedure -1- Perform the following operations in the unstructured data-matrix for each of the parties in turn: Regress electoral utility on the independent variable to be transformed Save the predicted value (the y-hat) Determine the mean of the y-hat in question Center the y-hat around 0 by subtracting mean Save, and use as one the variables to be stacked This should for each independent variable yield as many centered y-hats as there are parties to be stacked

9. 6-9 January 2005 Data Confrontation SeminarNottingham 9 Y-hat procedure -2- NB: the y-hat transformation may also be used to combine a set of indicators into a single stack-able independent variable e.g., define a multiple regression with utilities as dependent variable and as independents, e.g., occupation, income, autonomy in work, etc. in order to derive a single y-hat for job-status The y-hats contain exactly the same explanatory information as the original independent variable(s) as they are nothing else than a linear transformation of the original variable(s). Further details: see Tillie (1975), van der Eijk&Franklin (1996, ch.19-20), van der Eijk et al. (2005), van der Brug, van der Eijk &Franklin (forthcoming)

10. 6-9 January 2005 Data Confrontation SeminarNottingham 10 Empirical example -1- See dataset �stacking example.sav�, which is a subset of variables and of cases (the first 249 cases) from the German survey in EES99. It contains the following variables (see the codebook of EES99 for question texts etc.): identification of study, respondent and country political interest score (var078) electoral utility items for 6 parties (var081 to var086) left/right self-placement of respondent (var117) respondents� perceptions of left/right positions of 6 parties (in the same order as above) (var118 to var123) Of this a stacked dataset can be made with the stacked utility items as dependent variable and stacked left/right distances as independentcontinued-

11. 6-9 January 2005 Data Confrontation SeminarNottingham 11 Empirical example -2- The following syntax creates an identifier for parties: compute p1=1. compute p2=2. compute p3=3. compute p4=4. compute p5=5. compute p6=6. execute. And left/right distances are computed in SPSS for this dataset as follows: compute dist1=abs(var117-var118). compute dist2=abs(var117-var119). compute dist3=abs(var117-var120). compute dist4=abs(var117-var121). compute dist5=abs(var117-var122). compute dist6=abs(var117-var123). execute.

12. 6-9 January 2005 Data Confrontation SeminarNottingham 12 Empirical example -3- Enter the restructure procedure in the SPSS data menu. This brings you in a wizzard, with the following steps: First a choice of the kind of restructuring. Chose the 1st option (restructure selected variables into cases) 2nd step: define the number of variable groups, this is the number of stacked variables that will be created in the new datafile, each from a number of separate variables in the unstructured file. In our example, thew number is 3 (i.e.: the identification of parties �see previous sheet, the utilities of the parties (var082 to var086), and the left/right distances �see previous sheet) In step 3 you define the variables that have to be stacked, and you define their name in the stacked datamatrix. For example: Name 1st target variable �utility� and define var081 to var086 as the variables from which it will be constructed Name the 2nd variable lr_dist, and define dist1 to dist6 as the variables from which it will be constructed Name the 3rd variable id_pty, and define p1 to p6 as the variables from which it will be constructed continued

13. 6-9 January 2005 Data Confrontation SeminarNottingham 13 Empirical example -4- NB: for some reason beyond my comprehension, SPSS sometimes refuses to activate the Next> button after all the specifications in step 3. Retry a couple of times with deselecting and re-selecting the variables that have to be stacked, until the Next> button is activated and can be pressed, so as to enter you into the next step of the procedure Step 4 involves the creation of �index variables� which is the same as identifiers for the stacks. You have already done this by creating p1 to p6, so you may specify �none� (alternatively, you can not explicitly make the identifier, and here define 1 index variable) Step 6 asks what to do with the variables that are not to be stacked, and what to do with missing data When specifying �keep� for the non-selected variables, theur values are replicated for all new records that pertain to the same respondent (as you can see for yourself after completing this example) In the 2nd box choose �create a case�, as otherwise the resulting file becomes exceedingly non-transparant . Next step asks whether you want to restructure or to save syntax. In the latter case you have to execute the saved syntax from the syntax window In the data editor view of SPSS you now find the desired stacked data

14. 6-9 January 2005 Data Confrontation SeminarNottingham 14 References Eijk, C. van der, W. van der Brug, M. Kroh & M.N. Franklin 2005. �Rethinking the Dependent Variable in Voting Behavior � On the Measurement and Analysis of Electoral Utilities�, to appear in Electoral Studies, 2005. Eijk, C. van der , M. Franklin et al. 1996. Choosing Europe? The European Electorate and National Politics in the Face of the Union. Ann Arbor: University of Michigan Press (in particular Ch. 20) . Tillie, J. 1995. Party Utility and Voting Behavior. Amsterdam: Het Spinhuis.