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Chapter 4: Predictors of well-being

The advantage survey data holds over other, aggregated forms, is that we can go really bore down and unpick patterns of well-being based on individual living conditions and variables. Furthermore, using regression techniques, we can analyse the impact of several variables at the same time, allowing a full picture. For example, whilst analyses in Chapter 3 might suggest that income has a positive impact on a certain aspect of well-being, we might find that this effect does not emerge if we control for, let’s say, education levels.

Exercise 12

Let’s try an example. Perform a multiple regression with vitality as the dependent variable, and the following independent variables: gender, income (use the 12-band variable), level of education, and time spent watching TV. Remember, as usual, to weight correctly (in this case you need the combined weight as you are pooling across countries).

Solution SPSS

Using SPSS, you should get the following results:

Table 4.1. Coefficients
B* Std. Error* Beta** t Sig.
(Constant) .036 .020 1.784 .074
TV watching -.024 .002 -.082 -12.187 .000
Gender -.131 .008 -.112 -17.016 .000
Income .029 .002 .122 17.265 .000
Education .029 .003 .076 10.563 .000
  • Dependent variable: Vitality
  • *Unstandardised Coefficients
  • **Standardised Coefficients

All four variables are strongly significant. This shows that higher incomes and levels of education are associated with higher levels of vitality, whilst watching more TV is associated with lower levels of vitality. To interpret the gender variable you need to check how it is coded. In this case ‘1’ indicates male and ‘2’ indicates female. This means that, on average, females have vitality scores 0.131 lower than males. To generate these results, we used the following independent variables: TVTOT, GNDR, HINCTNT and EDULVL.

SPSS syntax

WEIGHT BY COMWEIGHT.
 
REGRESSION
/MISSING LISTWISE
/STATISTICS COEFF OUTS R ANOVA
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT vitality
/METHOD=ENTER tvtot gndr hinctnt edulvl.
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Structural equation modelling

The last section gives you the chance to try something a little different. We will be using a technique called structural equation modelling (SEM). SEM is a powerful statistical technique with a wide range of purposes, which allows one to simultaneously test several relationships at once, including factor structures, regression coefficients and between group differences. It also allows the incorporation of latent variables into models. SEM encourages confirmatory rather than exploratory approaches, and so is seen as a deductive scientific approach. Rather than having a set of data and seeing what is thrown up, using SEM effectively requires one to have a testable model before coming to the data. This makes it different from standard exploratory factor analysis, and some approaches to regression.

We will be using a package called AMOS, which is part of the SPSS suite of software. Not all of you will have access to this package.

The specific question we will be asking comes from a paper published on the relationship between well-being, income and aspirations1 (more on aspirations). Specifically, the paper argues that aspiratons mediate the relationship between income and well-being, such that for people who have more extrinsic aspirations, income will be more important in determining well-being, whilst for people who have more intrinsic aspirations, well-being will not be so determined by income. The paper found, using regression techniques, that there was indeed an interaction between income and aspirations in the determination of well-being, as operationalised by life satisfaction.

We will attempt to confirm these findings using a more robust methodology, which is possible through SEM (Multiple Group Analysis). Aspirations might have the opposite effect on a different independent variable. Perhaps, if income is less important for less materialistic individuals, then other determinants might be more important instead.

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Exercise 13

Before running AMOS, let’s look at the data set. You will notice a variable, called 'intrinsic_extrinsic', which operationalises the extent to which intrinsic aspirations dominate extrinsic aspirations for a given individual. Where an individual has stronger intrinsic aspirations than extrinsic ones, this figure will be positive - where they have stronger extrinsic aspirations than intrinsic ones, it will be negative. This variable is calculated from a subset of the Schwarz Portrait Values Questionnaire, which is included at the end of the ESS. For the syntax used to do this, see the appendix. The variable after this, is called 'intrinsic_extrinsic_bins', and it divides individuals into three roughly equal groups:

  1. Extrinsic: People who have stronger extrinsic aspirations than the European average
  2. Median group: People who have about the average level of extrinsic and intrinsic aspirations
  3. Intrinsic: People who have stronger intrinsic aspirations than the European average

Once you’ve seen this, make sure weighting is turned off (this is important for AMOS), close SPSS (if it is open) and run AMOS.

What we are going to do is to create a model, like a regression model, showing how three independent variables (gender, income and whether someone is living with a partner) determine life satisfaction. We will then see whether the coefficients estimated in this model are the same for people who are more extrinsically motivated as those who are more intrinsically motivated.

Let’s do the east bit first - uploading the data.

Start ‘Amos Graphics’.

Select ‘New’ from the ‘File’ menu.

Make yourself familiar with the tools on the toolbar on the left.

Select ‘Manage Groups’ from the ‘Analyze’ menu. A window will pop up, which should have ‘All’ (or ‘Group number 1’) written in it. Change ‘All’ (or ‘Group number 1’) to ‘Extrinsic group’. Then, create a new group (by clicking ‘New’) and call it ‘Intrinsic group’. Close the box. You should now see towards the left of the main window, two groups named extrinsic and intrinsic.

Next, we need to open our data file. On the toolbar on the left, click ‘Select data files’. A window will pop up, with the two groups named. For both groups click on the ‘File Name’ button and open the data set you have downloaded from Edunet.

Then click on the ‘Grouping Variable’ button and select from the long list ‘intrinsic_extrinsic_bins’ - this is the variable we saw earlier in SPSS. This must be done for both groups.

Lastly, for each group, click on the ‘Group Value’ button, and tell it the code for the two groups - for the extrinsic group it’s 1, and for the intrinsic group it’s 3. When you click ‘Ok’ (twice), the pop-up windows will close and, although you can’t see any change, you’ll hopefully have uploaded the data.

The next step is to draw the model. In this case, we have three independent variables, which are all observed, and an independent variable (also observed). Using the toolbar on the left, have a go at drawing the model, remembering to draw the arrows from the independent to the dependent variable. If you click on the ‘List variables in data set’ tool, you can drag variables into the boxes such that you should have something that looks like Figure 4.1:

Figure 4.1

You don’t have exactly that? Don’t worry about the labels of the boxes - as long as you have the right variables, that’s fine - they are 'GNDR', 'HINCTNT', 'PARTNER' and 'STFLIFE'. If you would like to modify the label of a variable, you can right-click the variable in the model and select ‘Object Properties’.

There are probably three things you need to add.

Firstly, you need to tell AMOS that we are prepared for correlations between the independent variables - those are the double-headed arrows on the left.

Secondly, you need to include a residual term - that’s the circle at the top-right. Without this, you would be implying that all the variation in life satisfaction is determined by these three independent variables, which is of course impossible. The residual is unobserved, which is why it gets a circle. Right-click the circle and select ‘Object Properties’. Label the circle ‘a1’ and set the ‘Mean’ to 0. The name ‘a1’ is arbitrary. The parameters attached to it (a mean of 0, and 1 on the arrow - you need to change the object properties to get at these) are also arbitrary but they’re needed to ‘identify’ the model. You don’t need to worry about this for now, but if you would like to know more about SEM, then this is quite important. In simple terms, these numbers are necessary because otherwise there are too many degrees of freedom and AMOS is unable to calculate a solution.

The last thing you need to add is probably the names for the arrows connecting the independents to the dependent. Again, they are arbitrary, but they are needed. Right-click the arrow and select ‘Object Properties’, write the name in the box ‘Regression weight’.

The model shown in Figure 4.1 is for the extrinsic group. To see the model for the intrinsic group, you need to select that group in the bar on the left. The model should look identical, but you’ll need to change the three names of the coefficients on the arrows. For example, ‘b1_ext’ should be changed to ‘b1_int’. If you haven’t already done so, to change these parameters for this group, you need to uncheck the ‘All groups’ tick box in the ‘Object Properties’ window. That way the coefficients will have different names in the two groups.

We’re almost there. Let’s see how we’re doing by running the model. First you should click ‘Analysis properties’ on the toolbar. Under the tab ‘Estimation’, make sure to select ‘Maximum likelihood’, ‘Fit the saturated and independence models’ and ‘Estimate means and intercepts’. Under ‘Output’, you should select ‘Minimization history’, ‘Standardized estimates’ and ‘Squared multiple correlations’. Close the ‘Analysis properties’ box.

Click the ‘Calculate estimates’ button. After thinking a little, you should see the output path diagram button light up with a red arrow (it’s one of the two buttons above your groups). Click on it and you should be able to see the results of the model! These will be shown on the diagram, but you can also click on the ‘View Text” option to see tables. Make sure to display the ‘Standardized estimates’ (below you groups).

Figure 4.2

Figure 4.3

Figures 4.2 & 4.3 show the different results for the two groups, using standardised estimates. The numbers on the arrows from the independent variables to the dependent variable, correspond to the familiar beta coefficients one gets when one does a normal multiple regression - indeed they should be the same as the ones you would get if you tried running the regression in SPSS or Nesstar. As you can see income is the strongest predictor of life satisfaction of the three chosen here, but it is less strong for the intrinsic group than for the extrinsic group. The other two variables are both dummy variables, and so one should check how they are coded in SPSS. As you’ll see, gender is coded 1 for male and 2 for female - a positive coefficient therefore would mean that females have higher life satisfaction. The partner dummy is actually coded in reverse, such that 1 means ‘yes’ and 2 means ‘no’. Therefore a positive coefficient means that people who live with their partners have lower life satisfaction. As you can see, both these dummy variables act in different directions for the two groups, albeit their effects are small (indeed, the small ‘with partner’ effect is not significant for the extrinsic group). Also, the number above the dependent variable (0.08 for the intrinsic group and 0.13 for the extrinsic group) tells us the fit of the model (equivalent to the R2 of a regression). This shows that, combined, these three objective variables are better at predicting life satisfaction amongst people with extrinsic aspirations, than those with intrinsic aspirations.

So far, nothing particularly special about SEM though. All this can be done in SPSS, or even Nesstar. But we still don’t know whether the differences between the two groups are significant. This is where SEM becomes useful. To see why, we need to work on our model again.

Click on the ‘View the input path diagram’ button to be able to edit the model.

We need, in fact, to create a new model. So far, we have allowed the two groups to be characterised by different coefficients. What if we told AMOS to hold the coefficients equal for the two groups, such that we didn’t allow the differences we have seen to emerge? This is similar to simply carrying out an analysis on all the data combined. The difference is that we allow the intrinsic-extrinsic variable to affect life satisfaction, simply that it cannot affect the relationship between the other independents and life satisfaction. We would then have two models - one like the one we’ve just seen, and one where the regression coefficients for the two groups are held equal. A priori, the first model will represent a better fit, as we are allowing AMOS to estimate freely more parameters. The question is whether it will be a much better fit. If it is significantly better, then we have confirmed that it is important to allow different beta coefficients for the two groups - i.e. that they are substantively different with respect to the model. If it is not significantly better, then, for sake of parsimony, we should assume that the same relationships between the independents and dependent hold in the two groups.

Let’s test this out. Select the ‘Manage Models’ option from the ‘Analyze’ menu. The model we have been using so far is called the ‘Default Model’. Rename it to call it ‘Test model’, but change nothing else.

Then click on the “New” button to create a new model. Call it ‘Baseline model’ - it will be the one where we constrain the regression coefficients such that they are the same for the two groups. This is where the names of the coefficients become useful. In the parameter constraints, tell AMOS that the regression coefficients for the intrinsic group are the same as those for the extrinsic group. If you have used the same names as we have, you should have something like this:

b1_int=b1_ext
b2_int=b2_ext
b3_int=b3_ext

Close the ‘Manage Models’ box.

Select ‘Analysis properties’ in the toolbox and make sure that ‘Modification indices’ is not selected in the Output’ tab.

Click ‘Calculate estimates’ in the toolbox.

As before, AMOS calculates coefficients for the ‘Test model’ both for the extrinsic and the intrinsic group. However, now it has also calculated coefficients for the ‘Baseline model’. The unstandardised regression coefficients for the two groups should now be identical (the standardised ones will be slightly different).

Now click on the “View Text” button in the toolbar. The key new statistic is the model comparison, which should look something like Table 4.2:

Table 4.2. Assuming Test model to be correct
Model DF CMIN P NFI Delta-1 IFI Delta-2
Baseline Model 3 53.664 .000 .018 .018

 

What this shows is that, the discrepancy between the groups (53.6) is sufficiently high as to be significant. In other words, the baseline model (where the two groups are assumed to have equal coefficients) is significantly poorer at modelling life satisfaction than the test model (where the two sets of coefficients are allowed to vary). It’s important to note that the baseline model does not assume values have no effect on life satisfaction (if you look at the ‘intercepts’ for life satisfaction for the two groups in the baseline model, you should see that the intrinsic group has a higher intercept than the extrinsic group - meaning that, all other things being equal, they have higher life satisfaction. It is just that the baseline model does not allow aspirations to influence the relationship between life satisfaction and the independent variables.

If you’re stuck then the solution is in this AMOS file

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Exercise 14

If you’ve made it this far, you might want to try out some variations on the model. Let’s look at two different dependent variables - the emotional well-being score, and the overall personal WBI. Simply change the dependent variable, and run the model again.

For emotional well-being, you should get the following sets of beta coefficients and the following estimation of discrepancy:

Table 4.3. Significant beta coefficients, emotional well-being
Independent variable Extrinsic group Intrinsic group
Income 0.301 0.188
Partner -0.053 -0.112
Gender -0.099 -0.065
Squared multiple correlations 0.117 0.069

 

Table 4.4. Estimation of discrepancy, emotional well-being
Model DF CMIN P
Baseline model 3 47.948 0.000

 

This time all the variables are significant for both groups, but again there is a clear difference in the influence of income on emotional well-being, with it playing almost twice as large a role for the extrinsic group. Interestingly, here, you get a clear difference between the importance of having a partner for the two groups - with the intrinsic group’s well-being more determined by this variable than the extrinsic group’s is. Also, again, the discrepancy between the test model and the baseline model is significant, therefore justifying separating out the two groups and claiming a meaningful difference.

Let’s try with vitality.

Table 4.5. Significant beta coefficients, vitality
Independent variable Extrinsic group Intrinsic group
Income 0.212 0.172
Partner   -0.027
Gender -0.143 -0.084
Squared multiple correlations 0.075 0.043

 

Table 4.6. Estimation of discrepancy, vitality
Model DF CMIN P
Baseline model 3 17.612 0.001

 

The discrepancy between the two models is still significant, but this time it is less so. This suggests, aspirations are less important in mediating the relationship between income and vitality than they are in mediating the relationship between income and emotional well-being or life satisfaction. It would be interesting to test, using SEM, whether the remaining mediation effect on vitality might be entirely down to the lower emotional well-being of people with more extrinsic values.

It would also be interesting to test these effects for individual nations, as the above calculations were done for the ESS data set as a whole.

If you’d like to try and learn more about SEM and using AMOS in general, you might want to work through the examples in the user guide, which can be found online.

The measurement of well-being is an evolving science. If you have any particular suggestions, please email them to saamah.abdallah@neweconomics.org.

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