Upload
others
View
2
Download
0
Embed Size (px)
Citation preview
Learn About Hierarchical Linear
Regression in SPSS With Data
From Prison Inmates
© 2019 SAGE Publications, Ltd. All Rights Reserved.
This PDF has been generated from SAGE Research Methods Datasets.
Learn About Hierarchical Linear
Regression in SPSS With Data
From Prison Inmates
Student Guide
Introduction
This example dataset introduces hierarchical linear regression, which is a
statistical technique used to explore the relationship between one outcome or
“criterion” variable (i.e., suicide ideation) and several predictor variables (i.e.,
depression, hopelessness, thwarted belongingness, perceived burdensome).
This example describes the nature and purpose of a hierarchical linear regression,
discusses the underlying assumptions of the analysis, and explains how to
conduct and interpret the findings of this analysis. We then illustrate a hierarchical
linear regression using data from a study testing the leading hypothesis of the
interpersonal theory of suicide among adult male prisoners (see Mandracchia
& Smith, 2015). Specifically, we examine the ability of a combination of two
maladaptive interpersonal cognitions (i.e., thwarted belongingness and perceived
burdensomeness) to statistically predict suicide ideation, after statistically
controlling for depression and hopelessness. This analysis is useful as it could
provide support for this theory as a comprehensive explanation for suicide ideation
by expanding its applicability to this high-risk population (i.e., incarcerated
offenders).
What Is Hierarchical Linear Regression?
Assessing the degree to which variables are related typically involves researchers
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 2 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates
examining the strength of associations between those variables using simple
correlations, simple linear regressions, and multiple linear regressions.
Hierarchical linear regression is a special case of a multiple linear regression in
which additional variables are entered into the equation in subsequent “blocks” to
draw conclusions about how these added predictor variables change the model’s
ability to statistically predict the criterion variable. This is often used in order to
evaluate whether one or more variables statistically predict a criterion variable
while statistically “controlling for” one or more other variables. For example,
after statistically controlling for socioeconomic status and level of educational
attainment, does race and gender predict US worker’s salaries? This is also
often used to investigate the potential presence of a moderating relationship of
a variable. For example, does the interaction of age and alcohol consumption
predict students’ grade point average (GPA) above and beyond age and alcohol
separately? The mathematical equations below represent two “blocks” of a
hypothetical hierarchical linear regression in which the second equation includes
the original predictor variables from the first equation along with an added
predictor variable (Tabachnick & Fidell, 2013).
(1)
Y ′ = A + β1X1 + β2X2 + e
(2)
Y ′ = A + β1X1 + β2X2 + β3X3 + e
In this dataset, we will discuss how to perform a hierarchical linear regression. As
a review, the regression equation defines Y ′ as the predicted value of the criterion
variable. The values of Xk are the predictors. A is the value of the y-intercept when
all the predictor variables have values of 0. The values of β are the best fitting
coefficients (also known as regression/beta coefficients or beta weights) assigned
to each predictor during the regression, and e represents the residuals (i.e.,
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 3 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates
error). This approach was used with the example data to investigate whether the
interaction of thwarted belongingness and perceived burdensomeness statistically
predicts suicidal ideation after statistically controlling for depression and
hopelessness among adult male prisoners. In this case, Y ′ would be the
predicted value of suicide ideation scores. Depression scale scores (X1) and
hopelessness scale scores (X2) are entered in Block 1, thwarted belongingness
scale scores (X3) and perceived burdensomeness scale scores (X4) are entered
into Block 2, and the interaction term of thwarted belongingness scale scores
multiplied by perceived burdensomeness scale scores (X5) is entered into Block
3.
Model Improvement
In hierarchical linear regression, variables that have been previously established
in the literature as being related to the criterion variable are entered into the first
block, followed in subsequent blocks by the remaining variables in order of best
known to least known. The idea being that the least known variables are the new
variables to explore as predictors. When one or more new variables are entered
into a subsequent block of the hierarchy, this produces a new, expanded model
(i.e., multiple linear regression equation). Each model produces a best fit line,
just as in other forms of regression. A comparison of the best fit lines of every
model (i.e., for each block in the hierarchy) is needed to identify the model with the
best fit to the data. As new variables are entered into the levels of the hierarchy,
the test of whether or not the model significantly improves is the objective of the
analysis. In other words, the models are compared to see whether the added
new variable(s) significantly add(s) to the ability of the model to statistically predict
the criterion variable. The improvement in predictability is evaluated based on
the extent to which R2 (i.e., the variance accounted for in the criterion variable)
increases significantly between each model of the hierarchy (Field, 2013). To
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 4 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates
determine whether the change in R2 is statistically significant, the F-ratio equation
is used:
(3)
Fchange = [(N – κnew – 1)R2
change] / [κchange(1 – R2
new)]In this equation, N is the total sample size, κnew is the number of new variables
added in the new model, and κchange is the difference in the number of variables
between the two blocks being compared (Field, 2013). The change in the F-ratio
is examined to determine statistical significance and whether the new model fit is
significantly improved by adding the new variable(s).
Assumptions
The main assumptions of hierarchical linear regression are the same as for other
forms of regression analyses. This includes that multicollinearity does not exist
or is only present at very low levels (Tabachnick & Fidell, 2013); this can be
assessed using the Durbin–Watson test for independence of residuals (Field,
2013). Researchers should also check plots of standardized residuals to evaluate
for assumptions of normality, homoscedasticity, linearity, independence of errors,
and absence of outliers.
Illustrative Example: Interpersonal Beliefs and Suicide Ideation
This example examines the relationship between beliefs about interpersonal
needs and suicide ideation in a sample of adult male prison inmates. Specifically,
it evaluates the ability of two independent but related beliefs from the interpersonal
theory of suicide to statistically predict suicide ideation. The two beliefs include
a diminished sense of belonging with other people (i.e., thwarted belongingness)
and the sense of being a burden to other people (i.e., perceived
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 5 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates
burdensomeness). The interpersonal theory posits that the strongest desire to
die (i.e., suicide ideation) is created by the combined experience of thwarted
belongingness and perceived burdensomeness. Because depression and
hopelessness have historically been widely stated as causes of suicide ideation,
the interpersonal theory states that thwarted belongingness and perceived
burdensomeness promote suicide ideation above and beyond depressed mood
and general hopelessness.
The research question for this example is:
• Among adult male prisoners, does the combination of thwarted
belongingness and perceived burdensomeness statistically predict suicide
ideation after accounting for depression and hopelessness?
The null Hypothesis is:
When statistically controlling for both depression and hopelessness, the
interaction term for thwarted belongingness and perceived
burdensomeness will not be statistically significantly related to suicide
ideation among adult male prisoners.
The Data
Data were obtained from 399 adult male prisoners and were collected via the
following self-report surveys with Likert-type response options:
• Depression was operationally defined as the total score from the Center for
Epidemiological Studies–Depression Scale (CES-D; Radloff, 1977); it has a
possible range of 0–60.
• Hopelessness was operationally defined as the score from the
Hopelessness Scale of the Depression, Hopelessness, and Suicide
Screening Form (DHS-H; Mills & Kroner, 2004); it has a possible range of
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 6 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates
0–10.
• Thwarted belongingness was operationally defined as the score from the
thwarted belongingness scale of the Interpersonal Needs Questionnaire
(INQ-TB; Van Orden, Cukrowicz, Witte, & Jioner, 2012); it has a possible
range of 9–63.
• Perceived burdensomeness was operationally defined as the score from
the perceived burdensomeness scale of the Interpersonal Needs
Questionnaire (INQ-PB; Van Orden et al., 2012); it has a possible range of
6–42.
• The interaction term of thwarted belongingness and perceived
burdensomeness was created by multiplying the total scores of these two
variables together for each participant; it has a possible range of 54–2,646.
• Suicide ideation was operationally defined as the total score from the Beck
Scale for Suicide Ideation (BSI); it has a possible range of 0–42 (Beck &
Steer, 1993).
The below histograms provide a visual display of the data distributions for the
variables in the hierarchical linear regression. In these figures, the mean and
standard deviation for each of the variables are also present.
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 7 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 8 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 9 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 10 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 11 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 12 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 13 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates
Analyzing the Data
The hierarchical linear regression was conducted in IBM® SPSS® Statistics
software (SPSS). Suicide ideation scores were entered as the criterion variable.
Depression scores and hopelessness scores were entered into the first block,
thwarted belongingness scores and perceived burdensomeness scores were
added in the second block, and the interaction term (thwarted belongingness ×
perceived burdensomeness) was added in the third block. Table 1 provides the
results from this analysis:
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 14 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates
Table 1: Results From the Hierarchical Linear Regression Predicting
Suicide Ideation.
Predictor ΔF(p) ΔR2 b β t (p)
Block 1 72.325 (<.001) .271
CES-D .125 .274 5.185 (<.001)
DHS-H .606 .312 5.906 (<.001)
Block 2 19.568 (<.001) .067
CES-D .079 .174 3.264 (.001)
DHS-H .413 .213 3.890 (<.001)
INQ-PB .186 .312 6.102 (<.001)
INQ-TB .001 .003 .056 (.955)
Block 3 6.147 (.014) .010
CES-D .083 .183 3.438 (.001)
DHS-H .381 .197 3.587 (<.001)
INQ-PB .017 .029 0.230 (.818)
INQ-TB −.057 −.129 −1.794 (.074)
INQ-PB × INQ-TB .005 .379 2.479 (.014)
Note: Bold values are statistically significant.
Presentation and Additional Interpretation of the Results
In regard to the hypothesis, the results of the analysis could be presented as:
“A hierarchical linear regression analysis was conducted to test the hypothesis
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 15 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates
that the interaction term for thwarted belongingness and perceived
burdensomeness would be statistically significantly related to suicide ideation
when statistically controlling for both depression and hopelessness. Scores for
depression and hopelessness were entered into the first block of predictor
variables, scores for thwarted belongingness and perceived burdensomeness
were added into the second block, and the interaction term (i.e., scores for
thwarted belongingness multiplied by scores for perceived burdensomeness) was
added into the third block. As predicted, the interaction term was significantly
related to suicide ideation (t = 2.479, p = .014), above and beyond the statistically
significant relations between depression (t = 5.185, p < .001) and hopelessness (t
= 5.906, p < .001) to suicide ideation, respectively. Overall, the full model (i.e., the
third block) accounted for nearly 35% of the variance in suicide ideation scores
(i.e., total R2 = .348).”
The information from the hierarchical linear regression analysis presented in Table
1 indicates the amount of variance in suicide ideation scores accounted for each
of the three blocks. Because each block of the hierarchical regression is its
own model, the increased ability of each model (i.e., each successive block in
the hierarchy) to statistically predict the criterion variable is presented as the
change in R2 values (ΔR2). In Block 1, which contains only depression and
hopelessness as predictors, the model accounts for 27.1% of the variance in
suicide ideation. When thwarted belongingness and perceived burdensomeness
are added to the model in Block 2, together all four predictors account for 33.8%
of the variance in suicide ideation (i.e., an additional 6.7%; R2 = .067). Finally,
when the interaction term (thwarted belongingness × perceived burdensomeness)
is added to the model in Block 3, together all five predictors account for 34.8% of
the variance in suicide ideation (i.e., an additional 1%; R2 = .010). As noted by
the change in F statistic (ΔF) for each block, each block is statistically significant
in providing added predictive ability for suicide ideation scores (above and beyond
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 16 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates
the previous block).
Review
Using self-report data collected from a sample of adult male prisoners, the
interaction between the maladaptive interpersonal cognitions of thwarted
belongingness and perceived burdensomeness was examined in relation to
suicide ideation. Hierarchical linear regression analysis is a robust approach to
assess the theoretical considerations of the interpersonal suicide. The analysis
provides evidence that participants’ experiences of thwarted belongingness and
perceived interactively predict suicidal ideation after controlling for participants’
depression and hopelessness.
Dataset learning outcomes:
• The type of research questions hierarchical liner regression can answer.
• Considerations and limits of the analysis.
• How to conduct a hierarchical linear regression.
• How to interpret change in R-squared.
Your Turn
You can download the sample dataset along with the How-to Guide showing you
how to conduct a hierarchical linear regression in SPSS. The sample dataset
includes the same variables as the illustrative example along with a new variable
called CES-D × DHS that represents the interaction term of depression and
hopelessness. Following the steps outlined in the How-to Guide, try running a
hierarchical linear regression in SPSS with the control variables and predictor
variables switched. That is, use thwarted belongingness and perceived
burdensomeness as the control variables and depression, hopelessness, and
their interaction term as the predictors of suicidal ideation. For additional practice
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 17 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates
conducting hierarchical linear regression in SPSS, you could then try to reproduce
the results presented in the illustrative example (i.e., with depression and
hopelessness as “control” variables, etc.).
References
Beck, A. T., & Steer, R. A. (1993). Manual for the Beck scale for Suicide Ideation.
San Antonio: Psychological Corporation.
Field, A. P. (2013). Discovering statistics using IBM SPSS statistics: And sex and
drugs and rock ‘n’ roll (4th ed.). Los Angeles, CA: SAGE.
Harrell, F. (2018, April 10). Problems caused by categorizing continuous
variables. Retrieved from http://biostat.mc.vanderbilt.edu/wiki/Main/
CatContinuous
Mandracchia, J. T., & Smith, P. N. (2015). The interpersonal theory of suicide
applied to male prisoners. Suicide & Life-Threatening Behavior, 45(3), 293–301.
Retrieved from http://doi.org/10.1111/sltb.12132
Mertler, C. A., & Vannatta, R. A. (2013). Advanced and multivariate statistical
methods (5th ed.). Glendale, CA: Pyrczak.
Mills, J. F., & Kroner, D. G. (2004). A new instrument to screen for depression,
hopelessness, and suicide in incarcerated offenders. Psychological Services, 1,
83–91. doi:http://dx.doi.org/10.1037/1541-1559.1.1.83
Radloff, L. S. (1977). The CES-D Scale: A self-report depression scale for
research in the general population. Applied Psychological Measurement, 1,
385–401. doi:http://dx.doi.org/10.1177/014662167700100306
Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.).
Boston, MA: Pearson Education.
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 18 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates
Van Orden, K. A., Cukrowicz, K. C., Witte, T. K., & Joiner, T. E. (2012).
Thwarted belongingness and perceived burdensomeness: Construct validity and
psychometric properties of the Interpersonal Needs Questionnaire. Psychological
Assessment, 24(1), 197–215. doi:http://dx.doi.org/10.1037/a0025358
Van Orden, K. A., Witte, T. K., Cukrowicz, K. C., Braithwaite, S. R., Selby,
E. A., & Joiner, T. E. (2010). The interpersonal theory of suicide. Psychological
Review, 117, 575–600. doi:http://dx.doi.org/10.1037/a0018697
SAGE
2019 SAGE Publications, Ltd. All Rights Reserved.
SAGE Research Methods Datasets Part
2
Page 19 of 19 Learn About Hierarchical Linear Regression in SPSS With Data From
Prison Inmates