In this guide, you will learn how to conduct a hierarchical linear regression in IBM® SPSS® Statistics software (SPSS) using a practical example to illustrate the process. You will find links to the example dataset, and you are encouraged to replicate this example. Several additional questions about this example are provided at the end of this guide to promote your exploration of this analysis even further. The example assumes you have already opened the data file in SPSS.
A hierarchical linear regression is a special form of a multiple linear regression analysis in which more variables are added to the model in separate steps called “blocks.” This is often done to statistically “control” for certain variables, to see whether adding variables significantly improves a model’s ability to predict the criterion variable and/or to investigate a moderating effect of a variable (i.e., does one variable impact the relationship between two other variables?). For example, you might want to know whether college students’ age and how much alcohol they drink are related to their current grade point average (GPA). You could use a “regular” multiple linear regression analysis to see whether this set of variables (i.e., age and alcohol use) predicts current GPA. However, what if you think the relationship between alcohol use and GPA is stronger for students who are younger than for students who are older (i.e., what if age moderates the relationship between alcohol use and GPA among college students)? In this case, you could use a hierarchical linear regression. In this analysis, GPA would be the outcome/criterion variable; in the first block, you would include only the two predictor variables independently (age and alcohol use), and in the second block, you would add a variable representing the interaction between age and alcohol use as a third predictor variable. If the interaction term (age × alcohol abuse) statistically predicts GPA above and beyond the two variables separately, then you can conclude there is a moderation effect.
This example represents a hierarchical linear regression using a set of variables from a study conducted by Mandracchia and Smith (2015) in which data from 399 adult male prisoners were used to explore the basic propositions of the interpersonal theory of suicide. Specifically, after accounting for depression and hopelessness (i.e., “control variables” entered into Block 1 of the analysis), the researchers investigated whether perceived burdensomeness and thwarted belongingness combined to statistically predict suicide ideation (i.e., criterion variable). In their study, perceived burdensomeness and thwarted belongingness were entered as separate variables in Block 2, and the interaction term (perceived burdensomeness × thwarted belongingness) was entered into Block 3. Refer to the corresponding Codebook for detailed information regarding these variables.
To produce a visual display of the dispersion of the data for each variable, you can create a histogram for each variable (including the interaction terms, in which two variables are simply multiplied together) in SPSS. To have SPSS create a series of histograms for these data (which are also provided previously in the Student Guide under the section titled The Data), select from the menu:
Analyze → Descriptive Statistics → Frequencies
Select each of the variables for which you want to produce a histogram (in this case, select all except Participant ID#) and click the right-directing arrow to move them into the box titled “Variable(s):”. Click on the box that says “Charts…” in the upper right corner and select Histograms. Click Continue, then OK. This will open another window which is your Output file that displays a series of Frequency Tables(one for each variable you selected), followed by a series of Histograms (one for each variable you selected). These histograms give you a graphical depiction of the overall shape, ranges, central tendencies, and patterns of the data for each of the variables selected.
To conduct the hierarchical linear regression analysis predicting suicide ideation as described in the Your Turn section of the Student Guide, select from the menu:
Analyze → Regression → Linear…
Figure 1 shows what this looks like in SPSS.
In the Linear Regression window that is now open, select “Total Score for Suicide Ideation [BSI_total]” and click on the blue arrow towards the top of the window to move it into the Dependent box (i.e., to select suicide ideation as the criterion variable). Then, select the “control” variables to be entered in Block 1 (i.e., total score for perceived burdensomeness [INQ_PB] and total score for thwarted belongingness [INQ_TB]) and click on the blue arrow in the middle of the screen to move them into the Independent(s) box; note that it says Block 1 of 1 in blue font above this box.
Figure 2 shows what this looks like in SPSS.
To select variables for Block 2 of the analysis, click on the blue box that says Next in the top right corner above the Independent(s) box; note the change to Block 2 of 2. Select both “control” variables that were included in Block 1 of 1 (i.e., total score for perceived burdensomeness [INQ_PB] and total score for thwarted belongingness [INQ_TB]) and also the two other predictor variables (i.e., total score for depression [CES-D_total] and total score for hopelessness [DHS_total]) and click on the blue arrow in the middle of the screen to move them into the Independent(s) box.
Figure 3 shows what this looks like in SPSS.
To select variables to include in the Block 3 of the analysis, click on the blue box that says Next in the top right corner above the Independent(s) box; note the change to Block 3 of 3. For this step/block, select all four variables that were included in Block 2 of 2 (i.e., total score for perceived burdensomeness [INQ_PB], total score for thwarted belongingness [INQ_TB], total score for depression [CES-D_total], and total score for hopelessness [DHS_total]), and also select the depression by hopelessness interaction term (i.e., interaction term for depression and hopelessness [CES-D × DHS]), and click on the blue arrow in the middle of the screen to move them into the Independent(s) box.
Figure 4 shows what this looks like in SPSS.
Before running the analysis, click on the Statistics box in the top right corner of the Linear Regression box. Select R squared change from the list on the right side of the Linear Regression: Statistics box. This will provide you with information about how much additional variance in the criterion variable (i.e., suicide ideation) is accounted for at each step/block in the hierarchical linear regression, and whether this is a statistically significant increase or not.
Figure 5 shows what this looks like in SPSS.
Click Continue to close out the Statistics box and then click OK at the bottom of the Linear Regression box to run the hierarchical linear regression analysis.
The output that SPSS produces for the above-described hierarchical linear regression analysis includes several tables. To interpret the findings of the analysis, however, you only need to focus on two of those tables.
The first table to focus on, titled Model Summary, provides information about each step/block of the analysis. You can see the Model Summary table below (Figure 6). Although data from each of the columns provide information about the analysis, the most critical information from this table appears in the following columns: R Square, R Square Change, and Sig. F. Change. Note that the first column, titled Column, indicates each step/block of the hierarchical linear regression (i.e., 1, 2, and 3). Block 1 (i.e., Model 1) has an R Square value of .328, which can be interpreted that thwarted belongingness and perceived burdensomeness scores account for 32.8% of the variance in suicide ideation scores. When depression and hopelessness scores were added in Model 2, the value for R Square increased to .414 (41.4% of the variance in suicide ideation scores accounted for by the four variables in the model). The column titled R Square Change (under Change Statistics) calculates this difference for you (i.e., .414 − .328 = .086). This can be interpreted that the addition of depression and hopelessness scores contributes 8.6% additional variance in suicide ideation accounted for, or explained, above and beyond that which was accounted for by only thwarted belongingness and perceived burdensomeness. To determine whether this is a statistically significant increase, look at the box on the far right side of the Model Summary table, titled Sig. F Change. Using a cutoff of p < .05, note that all three steps/blocks are statistically significant (p is less than .001), meaning that at each step/block, the inclusion of the additional variable(s) produces a statistically significant increase in variance accounted for in the outcome/criterion variable (i.e., suicide ideation). Note that the inclusion of the interaction term for depression and hopelessness in the third step/block accounts for a statistically significantly increased amount of variance in suicide ideation, which supports that a moderating effect is present.
The second table, to focus on (Figure 7) Coefficients, provides information about the individual predictor variables included in the model at each step/block of the analysis. Note that the predictor variables included in each step/block are identified in the first column on the left of the table, titled Model. As with all forms of regression analyses, for each predictor variable included in each step/block of the model, the coefficient represents the relationship that the individual predictor variable has with the criterion variable. This table provides both Unstandardized Coefficients and Standardized Coefficients, which are interpreted in the same manner as in other forms of regression analyses.
Using the dataset provided, follow the same steps described above to see whether you can replicate the results for this hierarchical linear regression analysis. What other variables are statistically significant in each step/block of the analysis, and how does the strength of the relationships between each predictor and outcome/criterion variable compare to the others? How much additional variance in suicide ideation scores is accounted for/explained by the interaction term for depression and hopelessness scores? How would you interpret these results given the new interaction term?
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