Exercise 2.1. A measurement equivalence test of the anti-immigration attitudes scale

In this exercise, we perform a test of measurement equivalence for the anti-immigration attitudes scale. We use the software package AMOS to estimate a MGCFA model for the three indicators. Our model will consist of 51 groups, namely 17 countries at three time points. We perform this analysis step-by-step, so that prior knowledge of AMOS is not required to perform the exercise. For more detailed information about AMOS, refer to the AMOS user’s guide [Arb05].

Step 1: Create a group membership variable

Before a multi-group model can be estimated in AMOS, we should perform one more preparatory step in SPSS: creating a variable that indicates the group to which a respondent belongs. Combine CNTRY and ESSROUND into a new variable, called GROUP. Hint: one possible way of doing this is to use the CONCAT function for merging string variables. Do not to forget to save your dataset afterwards.

SPSS Syntax

*Open the file you worked with in the first chapter and start where it ended. *Please do not forget to change ‘C:\’ to the path where you stored the ESS datasets.

GET FILE= 'C:\ESS123_immig.sav'.

*Create a new variable ‘group’, and define it as a character variable of length 12. *This variable will be the group membership variable.

STRING group (A12).

*Create a new variable ‘round_char’, and define it as a character variable of length 2. *round_char contains the same information as ESSROUND, but is a character variable. *This is necessary, because only character variables can be used with the CONCAT function.

STRING round_char (A2).
COMPUTE round_char = STRING(ESSROUND, F2.0).
EXECUTE.

*Merge the character variables cntry and round_char into a group. *The functions rtrim and ltrim are used to remove all blanks. *If the blanks are not removed, AMOS will run into problems at a later stage of the analysis. *Please do not forget to change ‘C:\’ to the path where you stored the ESS datasets.

COMPUTE group = CONCAT(rtrim(ltrim(cntry)),rtrim(ltrim(round_char))).
SAVE outfile = 'C:\ESS123_immig.sav'.

Step 2: Create groups and assign data

Save your work in SPSS and close the program.

AMOS is part of the SPSS software suite, but not all of you will have access to this package.

Open ‘AMOS Graphics’. This is AMOS’s graphical interface that makes it quite straightforward to perform multi-group analyses. Click ‘File > New’ to create a new Amos project. The first thing you do is to create 51 different groups. Click ‘Analyze > Manage groups...’.

Figure 2.1: 'Manage Groups' in Amos Graphics

The ‘Manage groups’ window pops up. This window can be used to create, delete and rename groups. Replace the text ‘Group number 1’ with the name of the first group (AT1). Next, click ‘New’ to create a new group and name it AT2. Continue until the 51 groups have been created. (The groups to be created are: AT1 AT2 AT3 BE1 BE2 BE3 CH1 CH2 CH3 DE1 DE2 DE3 DK1 DK2 DK3 ES1 ES2 ES3 FI1 FI2 FI3 FR1 FR2 FR3 GB1 GB2 GB3 HU1 HU2 HU3 IE1 IE2 IE3 NL1 NL2 NL3 NO1 NO2 NO3 PL1 PL2 PL3 PT1 PT2 PT3 SE1 SE2 SE3 SI1 SI2 SI3).

In the group pane, you can scroll through all groups that have been created. Check whether all necessary groups have been created. The next step consists of assigning data to the 51 groups. Click the ‘Select data file(s)’ tab.

Figure 2.2: 'Select data files' in Amos Graphics

The ‘data files’ window pops up. This window is used to specify what part of the dataset belongs to which group. Click on AT1 to select the first group. Now click ‘File Name’ and browse the SPSS dataset we created before (ESS123_immig.sav). Next, click ‘Grouping Variable’, and select the variable indicating group membership. In our case, this is the variable ‘GROUP’. Finally, click ‘Group Value’, and select the value that corresponds to the selected group (here: AT1). These steps should be repeated for all 51 groups (which can be a fairly time-consuming task). If the data are correctly assigned, the number of observations in the group should appear in the last column of the ‘Data Files’ window. Group AT1, for example, contains 1,677 observations (out of 84,331 in the complete data set).

Figure 2.3: Data files window in Amos Graphics

To avoid any risk of losing the work done, save the project (File > Save) under the name ‘basemodel’.

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References