Introduction to SPSS for the PC: Multivariate Analyses
Part 3: Multivariate Analyses
Within SPSS, analyses are generated using either menu
selections or command syntax. Below is a description of how to run
some common multivariate analyses using menu selections. Following
each description is the command syntax used to generate the same analyses
along with a brief explanation of the commands (For more help on using
syntax see: Tips
for SPSS Syntax). To generate the results utilized in these examples
you will need to download the files provided in the Raw
Data section below.
I. Multiple Regression
II. Multivariate Analysis of Variance (MANOVA)
III. Factor Analysis
I. Multiple Regression
Sample question: Does optimism, level of
income, and level of religiousity predict happiness? To answer this
question, you can run a multiple linear regression.
- Select Analyze > Regression > Linear from the menu bar to open the Linear Regression window.
- Highlight your dependent (or outcome) variable, happines, from the list of variables on the left, and click on the upper arrow to move it into the Dependent box.
- Highlight your independent (or predictor) variables, optimism, wealth, religiou, and move each into the Independents(s) box.
- Click on the Statistics button at the bottom of the Linear Regression window. A Linear Regression: Statistics window will appear. Click on the square next to the word Part and partial correlations (a check will now appear in the box in front of these words). Click Continue to return to the Linear Regression window.
- Click on OK to run the analysis. The results are printed below.
- Be sure that you can identify R, R2, F, df, p (the p-level is in the column labeled "Sig."), B, t, and pr to explain why the results are significant. For this analysis the results reveal that the three variables (level of income, level of religiousity, and optimism) together do significantly predict happiness, F(3, 200) = .5.411, p = .000, R2 = .175 (see ANOVA and Model Summary tables above). Examination of the Coefficients table indicate that the only variable that significantly predicts happiness is optimism, B = .203, pr = .412, t = 6.399, p = .000. The Coefficients table also provides the necessary information to generate the regression equation. For this example it is: happines = 2.770 - .027religiou - .076wealth + .203optimism.
Command Syntax for Regression:
REGRESSIONREGRESSION
/STATISTICS COEFF OUTS R ANOVA ZPP
/DEPENDENT happines
/METHOD=ENTER religiou wealth optimism .
/STATISTICS=COEFF OUTS R ANOVA ZPP- Refer to the command syntax for frequencies for an explanation of this subcommand. To get a complete list of the statistics offered for the regression analysis refer to the help menu in SPSS (i.e., Select Help > Topics on the menu bar which will open the Help Topics window. Click on the Index tab. Type "regression" in the box. Regression will appear in the second box. Highlight the Command Syntax under regression. Click on the Display button.).
/DEPENDENT happines - The "/dependent" subcommand identifies your dependent variable.
/METHOD=ENTER religiou wealth optimism. - The "/method=" subcommand identifies the type of regression analysis (enter runs the general regression) as well as identifies your independent or outcome variable(s).
II. Multivariate Analysis of Variance (MANOVA)
Sample question: Are there differences in participants'
self-reported happiness, as measured by the three subscales of happiness,
based on one's gender and the number of friends a person has (fewer than
five or more than six)? To answer this question you can run a multivariate
ANOVA, with the happiness subscales as the dependent variables and friends
and gender as the independent variables.
- Select Analyze > General Linear Model > Multivariate from the menu bar to open the Multivariate window.
- Highlight your first dependent variable, subhap1, from the list of variables on the left, and click on the upper arrow button to move it into the Dependent Variables box. Add the remaining two variables, subhap2 and subhap3, in the same fashion.
- Highlight your first independent variable, friends, from the list of variables on the left, and click on the middle arrow button to move it into the Fixed Factor(s) box. Add the remaining variable, gender, in the same fashion.
- Click on the Options button. An Options window will appear. Click on the square next to the word Descriptive (a check will now appear in the box). This will cause descriptive statistics to print out along with your ANOVA results (If you don't do this, the printout will only tell you if the overall ANOVA is significant, but it will not tell you the means of each group.). Also click on the square next to the word Homogeneity tests. This will test the assumption of homogeneity of variance.
- Click on Continue to return to the Multivariate window.
- Click on OK to run the analysis. Selected results are printed below.
- Be sure you can identify n, M, and SD for each of the independent variables and the friends by gender interaction in the descriptive statistics output.
- Examine Box's Test for Equality to determine if the homogeniety of variance assumption is met. If the p-value is less than .001 (look under Sig.) then the the assumption has been violated. If this assumption is violated, talk to your instructor about how to address this violation.
-
Examine the Multivariate Tests table to determine the significance
of your omnibus test. That is, when you take the composite of all
the subscales of happiness is there a significant difference for each of
the main effects and interaction effect. To determine the significance
of the test you examine Wilk's Lambda (
),
F, and p. In this case, there is a significant difference
in level of happiness (collapsed across the three happiness subscales)
based on the number of friends a person has, =
.828, F(3, 198) = 13.68, p = .001. There is also a
significant difference in level of happiness (collapsed across the three
happiness subscales) for gender and the interaction of gender and friends. - Since the results of the MANOVA are significant, you will want to examine the Test of Between Subjects Effects table to determine whether the independent variables are significant for each happiness subscale. Examination of the Test of Between Subjects Effects table indicates that there was a significant difference in all three subscales of happiness for the friends variable. However, note that for the gender variable happiness subscale 1 is not significant. Be sure you can identify the F, df, and p (the p-value is in the column labeled "Sig.") for each test. For example, individuals with more than six friends had a higher happiness score on the first subscale (M = 3.77, SD = 1.05) than those with fewer than five friends (M = 3.12, SD = 1.16) , F(1, 200) = 17.61, p = .001.
- If there are more than two levels of an independent variable then multiple comparisons would need to be conducted (see the One-way ANOVA, for directions on how to add post-hoc tests). In this case for the main effects, you can examine the Descriptive Statistics table. However, to determine where the differences lie in the interaction effect, you will need to perform the appropriate hand calculations.
Command Syntax for Multivariate ANOVA:
Back to Multivariate Analyses listGLMGLM
subhap1 subhap2 subhap3 BY friends gender
/PRINT = DESCRIPTIVE ETASQ HOMOGENEITY
/DESIGN = friends gender friends*gender .
subhap1 subhap2 subhap3 BY friends gender - This statement indicates the independent and dependent variables to be utilized when conducting the MANOVA. The dependent variables are listed first followed by the independent variables with "By" separating the two.
/PRINT = DESCRIPTIVE ETASQ HOMOGENEITY - The "/print=" subcommand allows the user to print several descriptive and inferential statistical tests that may be important to examine when running a MANOVA. To get a complete list of the statistics offered for the MANOVA refer to the help menu in SPSS (i.e., Select Help > Topics on the menu bar which will open the Help Topics window. Click on the Index tab. Type "GLM" in the box. GLM Multivariate will appear in the second box. Highlight Options under GLM Multivariate. Click on the Display button.).
/DESIGN = friends gender friends*gender. - The "/design=" subcommand identifies the main and interaction effects to be analyzed. To examine main effects you just need to list the variable name (e.g., gender or friends). To examine interaction effects you list the variables you want to interact with a "*" between the variables (e.g., gender*friends).
III. Factor Analysis
Sample question: Do each of the three subscales
represented in the happiness scale form an independent pattern of correlations
delineating them as separate factors? That is, if you examined the
correlations between all items on the happiness scales, would the correlations
be stronger for items that represent each of the single subscales?
Or more precisely, what is the relationship among the happiness items?
Do thematic categories emerge? To answer this question you can run
a Factor Analysis including all the happiness items.
- Select Analyze > Data Reduction > Factor from the menu bar to open the Factor Analysis window.
- Highlight all of the happiness items, hap1 through hap12 from the list of variables on the left, and click on the upper arrow button to move it into the Variables box.
- Click on the Rotation button. A Factor Analysis: Rotation window will appear. Click on the circle next to the word Direct Oblimin (a check will now appear in the circle). This will prompt SPSS to rotate the solution to find the best fit for the data while allowing the factors to correlate. If you do not want the factors to correlate click on Varimax instead.
- Click on Continue to return to the Factor Analysis window.
- Click on OK to run the analysis. Selected results are printed below.
- Examine the Total Variance Explained table to determine how many factors emerged from the data. To determine the number of factors look at the second column which represents the Eigenvalues. As you can see there can be as many factors as there are items (i.e., there are 12Eigenvalues and 12 items on the happiness scale). However, you want to interpret meaningful factors. One way to identify meaningful factors is to examine only those factors that have an Eigenvalue that is greater than 1. In this case, there are three viable factors.
- To determine which items fall into each of the three factors we examine the Pattern Matrix table (the Component Matrix table includes the items before the rotation occurred and is therefore not interpretable). As you look at the Pattern Matrix you will notice that there are three columns, one to represent each of the three factors with Eignevalues greater than 1. Look at the first item (i.e., I feel life is very rewarding). You will see a number in each of the three columns. These numbers are called fator loadings. If an item has a factor loading greater than .30 in any of the columns it is considered to be representative of that factor. For example, the first item is representative of the second factor.
- Once you have identified the items in a particular factor, you will need to identify the underlying meaning of the factor. In this case, you will need to determine what type of happiness is being tapped by each of the three factors.
- Note: If an item has a factor loading of .30 or higher in more than one column, it is considered to cross load, meaning it is representative of both factors. Talk to your instructor about reasonable methods for handling items that cross load.
Command Syntax for Factor Analysis:
FACTOR
/VARIABLES hap1 hap2 hap3 hap4 hap5 hap6 hap7 hap8 hap9 hap10 hap11 hap12
/ROTATION OBLIMIN .
FACTOR
/VARIABLES hap1 hap2 hap3 hap4 hap5 hap6 hap7 hap8 hap9 hap10 hap11 hap12 - the "variables" statement indicates which variables are to be included in the analysis.
/ROTATION OBLIMIN. - the "rotation" statement identifies which rotation method to use. In this case the oblimin rotation is used.
Back to Multivariate
Analyses list
To illustrate how to conduct multivariate analyses you will use the following hypothetical data set. The data set contains a 12-item survey measuring happiness along with potential indicators of happiness including religiousity, level of income, optimism, number of friendships and gender. You can either download the SPSS data file or an equivalent Excel file that can be transfered to SPSS (see the files below). To open SPSS Files you will need to make sure SPSS 11.0 is installed on the computer. If SPSS is installed, open the SPSS file using Internet Explorer (Netscape Navigator will not work). To do this, right click on the SPSS link and choose "Save Target As..." and choose a location and file name for the file. Then open up the file in SPSS. If SPSS is not installed on the computer, open the alternative Excel document. The data from an Excel spreadsheet can be later transferred to an SPSS data file, however, the variable information will need to be re-entered (see the variable names and coding below). Please refer to Setting Up Data Files to define variables and enter data into SPSS.
Multivariate SPSS Data File
Multivariate Excel Data File
| Variable Name | Description and Coding |
| id | participant identification number |
| hap1 | I feel that life is rewarding (1=strongly disagree to 5 = strongly agree) |
| hap2 | I often experience joy and elation (1=strongly disagree to 5 = strongly agree) |
| hap3 | I feel I have a great deal of energy (1=strongly disagree to 5 = strongly agree) |
| hap4 | Life is good (1=strongly disagree to 5 = strongly agree) |
| hap5 | I am very happy (1=strongly disagree to 5 = strongly agree) |
| hap6 | I feel fully mentally alert (1=strongly disagree to 5 = strongly agree) |
| hap7 | I laught a lot (1=strongly disagree to 5 = strongly agree) |
| hap8 | I rarely wake up feeling rested (reversed score) (1=strongly disagree to 5 = strongly agree) |
| hap9 | I am satisfied about everything in my life (1=strongly disagree to 5 = strongly agree) |
| hap10 | I find most things amusing (1=strongly disagree to 5 = strongly agree) |
| hap11 | I feel able to take anything on (1=strongly disagree to 5 = strongly agree) |
| hap12 | I do not think that the world is a good place (reversed score) (1=strongly disagree to 5 = strongly agree) |
| subhap1 | Subscale Happiness 1 |
| subhap2 | Subscale Happiness 2 |
| subhap3 | Subscale Happiness 3 |
| religiou | Level of Religiousity (1=not very religious at all to 7=very religious) |
| wealth | Level of Income (1=under 20,000, 2=21,000-40,000, 3=41,000-60,000, 4=61,000-80,000, 5=81,000-100,000, 6=over 100,000) |
| optimism | Optimism Score (1=low optimism to 7 = high optimism) |
| friends | Number of Friendships (1=five or fewer, 2=six or more) |
| gender | Gender (1 = female, 2 = male) |
