The main purpose of a multigroup analysis is to find out the extent to which groups differ. Do the groups all have the same path diagram with the same parameter values?
Do the groups have the same path diagram but with different parameter values for different groups? Does each group need a different path diagram? Amos Graphics has the following conventions for specifying group differences in a multigroup analysis:
All groups have the same path diagram unless explicitly declared otherwise.
Unnamed parameters are permitted to have different values in different groups.
Thus, the default multigroup model under Amos Graphics uses the same path diagram for all groups but allows different parameter values for different groups.
Parameters in different groups can be constrained to the same value by giving them the same label. (This will be demonstrated in Model B on p. 172.)
Specifying Model A
E From the menus, choose File → New to start a new path diagram.
E From the menus, choose File → Data Files.
Notice that the Data Files dialog box allows you to specify a data file for only a single group called Group number 1. We have not yet told the program that this is a multigroup analysis.
E Click File Name, select the Excel workbook UserGuide.xls that is in the Amos Examples directory, and click Open.
E In the Select a Data Table dialog box, select the Attg_yng worksheet.
E Click OK to close the Select a Data Table dialog box.
E Click OK to close the Data Files dialog box.
E From the menus, choose View → Variables in Dataset. E Drag observed variables recall1 and cued1 to the diagram.
E Connect recall1 and cued1 with a double-headed arrow.
E To add a caption to the path diagram, from the menus, choose Diagram → Figure Caption and then click the path diagram at the spot where you want the caption to appear.
E In the Figure Caption dialog box, enter a title that contains the text macros \group and
\format.
E Click OK to complete the model specification for the young group.
E To add a second group, from the menus, choose Analyze → Manage Groups.
E In the Manage Groups dialog box, change the name in the Group Name text box from Group number 1 to young subjects.
E Click New to create a second group.
E Change the name in the Group Name text box from Group number 2 to old subjects.
E Click Close.
E From the menus, choose File → Data Files.
The Data Files dialog box shows that there are two groups labeled young subjects and old subjects.
E To specify the dataset for the old subjects, in the Data Files dialog box, select old subjects.
E Click File Name, select the Excel workbook UserGuide.xls that is in the Amos Examples directory, and click Open.
E In the Select a Data Table dialog box, select the Attg_old worksheet.
E Click OK.
Text Output
Model A has zero degrees of freedom.
Amos computed the number of distinct sample moments this way: The young subjects have two sample variances and one sample covariance, which makes three sample moments. The old subjects also have three sample moments, making a total of six sample moments. The parameters to be estimated are the population moments, and there are six of them as well. Since there are zero degrees of freedom, this model is untestable.
Chi-square = 0.000 Degrees of freedom = 0
Probability level cannot be computed
Computation of degrees of freedom (Default model)
Number of distinct sample moments: 6 Number of distinct parameters to be estimated: 6 Degrees of freedom (6 - 6): 0
To view parameter estimates for the young people in the Amos Output window:
E Click Estimates in the tree diagram in the upper left pane.
E Click young subjects in the Groups panel at the left side of the window.
To view the parameter estimates for the old subjects:
E Click old subjects in the Groups panel.
Graphics Output
The following are the output path diagrams showing unstandardized estimates for the two groups:
The panels at the left of the Amos Graphics window provide a variety of viewing options.
Covariances: (young subjects - Default model)
Estimate S.E. C.R. P Label recall1 <--> cued1 3.225 .944 3.416 ***
Variances: (young subjects - Default model)
Estimate S.E. C.R. P Label
recall1 5.787 1.311 4.416 ***
cued1 4.210 .953 4.416 ***
Covariances: (old subjects - Default model)
Estimate S.E. C.R. P Label recall1 <--> cued1 4.887 1.252 3.902 ***
Variances: (old subjects - Default model)
Estimate S.E. C.R. P Label
Click either the View Input or View Output button to see an input or output path diagram.
Select either young subjects or old subjects in the Groups panel.
Select either Unstandardized estimates or Standardized estimates in the Parameter Formats panel.
Model B
It is easy to see that the parameter estimates are different for the two groups. But are the differences significant? One way to find out is to repeat the analysis, but this time requiring that each parameter in the young population be equal to the corresponding parameter in the old population. The resulting model will be called Model B.
For Model B, it is necessary to name each parameter, using the same parameter names in the old group as in the young group.
E Start by clicking young subjects in the Groups panel at the left of the path diagram.
E Right-click the recall1 rectangle in the path diagram.
E From the pop-up menu, choose Object Properties.
E In the Object Properties dialog box, click the Parameters tab.
E In the Variance text box, enter a name for the variance of recall1; for example, type var_rec.
E Select All groups (a check mark will appear next to it).
The effect of the check mark is to assign the name var_rec to the variance of recall1 in all groups. Without the check mark, var_rec would be the name of the variance for recall1 for the young group only.
E While the Object Properties dialog box is open, click cued1 and type the name var_cue for its variance.
E Click the double-headed arrow and type the name cov_rc for the covariance. Always make sure that you select All groups.
The path diagram for each group should now look like this:
var_rec recall1
var_cue cued1
cov_rc
Example 10: Model B Homogenous covariance structures
in two groups, Attig (1983) data.
Model Specification
Text Output
Because of the constraints imposed in Model B, only three distinct parameters are estimated instead of six. As a result, the number of degrees of freedom has increased from 0 to 3.
Model B is acceptable at any conventional significance level.
The following are the parameter estimates obtained under Model B for the young subjects. (The parameter estimates for the old subjects are the same.)
You can see that the standard error estimates obtained under Model B are smaller (for the young subjects, 0.780, 0.909, and 0.873) than the corresponding estimates obtained under Model A (0.944, 1.311, and 0.953). The Model B estimates are to be preferred over the ones from Model A as long as you believe that Model B is correct.
Chi-square = 4.588 Degrees of freedom = 3 Probability level = 0.205
Computation of degrees of freedom (Default model)
Number of distinct sample moments: 6 Number of distinct parameters to be estimated: 3 Degrees of freedom (6 - 3): 3
Covariances: (young subjects - Default model)
Estimate S.E. C.R. P Label recall1 <--> cued1 4.056 .780 5.202 *** cov_rc
Variances: (young subjects - Default model)
Estimate S.E. C.R. P Label
recall1 5.678 .909 6.245 *** var_rec
cued1 5.452 .873 6.245 *** var_cue
Graphics Output
For Model B, the output path diagram is the same for both groups.
Modeling in VB.NET
Model A
Here is a program (Ex10-a.vb) for fitting Model A:
Sub Main()
Dim Sem As New AmosEngine Try
Sem.TextOutput()
Sem.BeginGroup(Sem.AmosDir & "Examples\UserGuide.xls", "Attg_yng") Sem.GroupName("young subjects")
Sem.AStructure("recall1") Sem.AStructure("cued1")
Sem.BeginGroup(Sem.AmosDir & "Examples\UserGuide.xls", "Attg_old") Sem.GroupName("old subjects")
The BeginGroup method is used twice in this two-group analysis. The first BeginGroup line specifies the Attg_yng dataset. The three lines that follow supply a name and a model for that group. The second BeginGroup line specifies the Attg_old dataset, and the following three lines supply a name and a model for that group. The model for each group simply says that recall1 and cued1 are two variables with unconstrained variances and an unspecified covariance. The GroupName method is optional, but it is useful in multiple-group analyses because it helps Amos to label the output in a meaningful way.
Model B
The following program for Model B is saved in Ex10-b.vb:
The parameter names var_rec, var_cue, and cov_rc (in parentheses) are used to require that some parameters have the same value for old people as for young people. Using the name var_rec twice requires recall1 to have the same variance in both populations.
Similarly, using the name var_cue twice requires cued1 to have the same variance in both populations. Using the name cov_rc twice requires that recall1 and cued1 have the same covariance in both populations.
Sub Main()
Dim Sem As New AmosEngine Try
Dim dataFile As String = Sem.AmosDir & "Examples\UserGuide.xls"
Sem.Standardized() Sem.TextOutput()
Sem.BeginGroup(dataFile, "Attg_yng") Sem.GroupName("young subjects") Sem.AStructure("recall1 (var_rec)") Sem.AStructure("cued1 (var_cue)") Sem.AStructure("recall1 <> cued1 (cov_rc)") Sem.BeginGroup(dataFile, "Attg_old")
Sem.GroupName("old subjects")