Instructions

This section contains the following topics:

1) Continuous moderator example;

2) Categorical moderator example;

3) Simple slope computations;

4) Display of results; and

5) References;

1. Continuous moderator example
In the following continuous moderator example, I will be describing a set of data where depression, a continuous variable, is considered to be the dependent variable. Stress, a continuous variable, is considered to be the main effect. Social support coping, a continuous variable, is considered to be the moderating variable, i.e., the variable that affects the linear relationship between stress and depression. This example is considered to be a "continuous moderator" case because the moderating variable is continuous.

Thus, if one was interested in determining whether social support moderates the influence of stress upon depression, one would choose "Continuous Data Entry" in the first menu. The next menu asks for one to enter labels for the graph and statistical information.

Labels. The four labels are: 1) the descriptive label that goes at the top of the graph (e.g., Moderation of the Effect of Stress on Depression by Social Support); 2) the X axis label (e.g., Stress); 3) the Y axis label (e.g., Depression); and 4) the name of the moderating variable (e.g., Social support). Note that it is standard practice to display the main effect on the X axis, the dependent variable on the Y axis, and the moderating variable (in this case, social support) is represented by the three lines that are plotted on the graph.

Statistical information. The rest of the menu requires that one input information taken from the regression analysis output. In particular, one must enter the unstandardized regression coefficient (B), the mean, and the standard deviation of both stress (the main effect) and social support (the moderating variable). In addition, the menu page requires the B for the interaction term and the constant. All of the Bs can be obtained from the multiple regression output generated by your software package, and the means and standard deviations may be computed in a simple descriptive statistics run on the same data.

A commonly discussed issue concerns the means of the two continuous variables. Aiken and West (1991) and others recommend that the two continuous variables be centered for use in this type of analysis because the resulting graph will be centered on the mean for both the IV and the ModV. Doing so permits an easier interpretation of the pattern (sometimes). However, it is not essential to center your IV and ModV, but some users may wish to do so. If you choose to remove the mean from each variable, do so in the statistical package that your data reside in. Simply perform a compute statement in which the mean (e.g., 5.15) is subtracted from every value in a given column. Common practice is to subtract the mean from the IV as well as the ModV before one creates the interaction term by multiplying these two variables together. Note that the standard deviations of these two main effects are unchanged by centering. I could have stipulated in this menu that the means were 0.00 for the first two variables, but decided against this because some users may wish to create charts that would not require centered variables.

Be careful that you enter the unstandardized regression coefficients (the Bs) instead of the betas. When you are transferring information from the statistical output to ModGraph, be careful that you note the order that the variables are listed in the output. For example, SPSS output lists the constant first instead of last.

After you have entered all of these fields, hit the CALCULATE button and the computed means will be displayed in the 3 X 3 table at the bottom of the page. Hit SEE FIGURE, and the graph should be displayed. The graph is a .jpeg file which can be copied and pasted into your own documents if you wish. If you would like to examine the cell means, click on DATA ENTRY in the menu at the left of the page. This will take you back to the first page. The 3 X 3 matrix will contain the computed cell means that were used to create the figure. If you do not wish to use the .jpeg-based figure here, you can use these means to create a graph in Word or other program.

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2. Categorical moderator example
If one wishes to depict an interaction between a continuous variable and a two-level categorical variable (e.g., stress experienced by Chinese-American and European-American subjects as it affects depression), then one would choose the Categorical Data Entry option on the first menu. The menu is similar as for the continuous moderator, but there are a few differences. For example, one would type in the name of the group that receives a dummy code of 1, and similarly for the group that is determined to be the comparison group (it receives a value of 0). As with the continuous data menu, one is then required to enter Bs, means, and standard deviations where appropriate. One may wish to center the IV (which is continuous), but one would not center the ModV, of course, because it is a dummy-coded categorical variable.

Several points need to be considered in this case as opposed to the continuous option. First, the categorical variable (whether gender, ethnic group, clinical diagnostic category, etc.) is considered to be the moderator. Second, the mean and standard deviation of the categorical variable are not requested because it is nonsensical in this case. However, you need to be clear as to the labeling of the comparison and the dummy-coded groups. Be sure that the coding of 0 and 1 are congruent with your dummy coded variable in the original dataset. In other words, you should have coded your categorical variable in your dataset as 0 or 1, and then multiplied it by the continuous IV. If you coded your categorical variable in your dataset as 1 and 2, then you have a problem. The ModV should be properly dummy-coded, i.e., at least one value should be zero. Third, your categorical ModV must have only two dummy-coded groups (e.g., depressed vs. personality disordered patients). The program, as currently constituted, cannot handle the three (or more) group case yet, but this improvement is countenanced and hopefully can be included in later versions.

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3. Simple slope computations
In interpreting the meaning of a figure, it is often important to know the values of the simple slopes, and to know whether these slopes differ significantly from zero. So, after the figure has been generated, go to the appropriate "Simple Slopes Computations" page (this can be found in the menu on the left hand side of the page). This page brings forward (in the upper right-hand corner) relevant information already entered in the data entry page, and asks for additional information to be supplied. After these critical items are entered, simply click on "CALCULATE" and simple slopes, standard errors, the degrees of freedom, t-values, and associated p-values are displayed.

The uninitiated user may be puzzled by the task of providing these new items of information. Here are some helpful hints. First, when you run the regression analysis, request output to include the "covariance matrix". Second, when this is obtained, search for the three critical items of statistical information. In statistical parlance, the matrix is an Sb matrix, where b refers to the number of coefficients examined in the regression model (3 in both the continuous and categorical examples). The matrix will look similar to this:

It is useful to know that "variance" refers to a cell in which the variable is arrayed against itself (e.g., b1 by b1), and "covariance" refers to a cell in which one variable is arrayed against another variable (e.g., b1 by b3).

In this example, b1 refers to the regression coefficient for the main effect, b2 refers to the coefficient for the moderator, and b3 refers to the coefficient for the interaction term. s11 refers to the variance of the main effect (the number in the upper left hand corner, -.467); s33 refers to the variance of the interaction term (the number in the lower right hand corner, -.891); and s13 refers to the covariance between the main effect and the interaction term (the number in the upper right hand corner, .047). Thus, one should examine the variance-covariance table that is generated by your statistical program, and after making sure that the matrix is constructed in the way described above, select the three items and transfer them to the program. The number of subjects can be obtained by running a frequencies analysis on the data.

A warning: be sure that your output conforms to this particular arrangement. SPSS will occasionally re-order the variables, particularly in complicated dummy-coded analyses. If it creates a differently ordered matrix, simply identify the two relevant variances and the one relevant covariance, and then input these into ModGraph.

Another warning: SPSS and some other programs will output in the covariance matrix a value such as this: .000. The SPSS default seems to be three decimal points for variances and covariances, so very small numbers will be rounded up to .000. In actual fact, .000 is numerically the same as zero, and I have to warn you that entering .000 into ModGraph will cause a problem. The reason for this problem is that covariances cannot actually be a true zero value. So, if you enter .000 into ModGraph, it will treat this value as zero and will generate false outputs. Consequently, please do not enter .000 as a value.

So what should one do? With SPSS, if you double-click on the matrix, or a value in the matrix, the program will open it up and give you the value to 12 or 15 decimal places. For example, .000 might become .000001756. In this case, just enter the value. Occasionally SPSS will give values in scientific notation, e.g., 1.7869E-6. When you obtain a value like this, you can convert it back to regular notation. The "E-6" tells you to move the decimal point to the left six places. Thus, 1.7869E-6 becomes .0000017869, and you should enter this value into ModGraph.

Let's assume that you do all of this correctly; then the outputted values at the bottom of the page will include the simple slopes and the associated t- and p-values. If the p-value is less than .05, then you can conclude that the slope of that particular line significantly varies from 0.

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4) Display of Results
In the continuous moderator example, the figure displays the IV main effect (i.e., stress) along the X-axis, and the moderating variable is depicted with three lines designated as high, medium, and low. The three levels of high, medium, and low (for both the continuous main effect as well as the continuous moderating variable) are computed using the mean as the medium value, one standard deviation above the mean as the high mean, and one standard deviation below the mean as the low mean (following Aiken & West, 1991).

In the categorical data example, the figure displays the main effect (i.e., stress) along the X-axis, and the moderating variable is depicted with two lines designated as the two groups. The continuous data example should display symmetry among the three lines, but the categorical data example may not display symmetry between the two lines.

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5) References
For additional information and assistance, refer to these readings:

Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions.

Newbury Park, CA: Sage.

Conceptual, strategic, and statistical considerations.Journal of Personality and Social Psychology, 51, 1173-1182.

Hillsdale, NJ: Lawrence Erlbaum and Associates.

"Masculinity, femininity, and psychosocial adjustment in medical students: A 2-year follow-up". Journal of Personality Assessment, 53, 583-599.

Examples from the child-clinical and pediatric psychology literatures. Journal of Consulting and Clinical Psychology, 65, 599-610.

Journal of Pediatric Psychology, 27, 87-96.