AIM command in SPSS Statistics explores cluster (or other groups) profiles and assesses feature importance in differentiating clusters/groups.

AIM groupvar /CONTINUOUS scalevar /PLOT ERRORBAR.

will plot the scalevar's means + confidence intervals by the groups of groupvar.

The confidence intevals plotted are the "simultaneous" CIs, they are wider than the usual, individual CIs, because for each group they include the information that there are several groups. But what is the specific formula these simultaneous CIs are computed by? and what is the idea behind it? I could not find any explanation in Algorithms (AIM chapter or "Cluster Evaluation" chapter) and in CSR (AIM command). Please, give the formula here and also add it to the Algorithms document (AIM command).

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Kirill Orlov
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AIM command in SPSS Statistics explores cluster (or other groups) profiles and assesses feature importance in differentiating clusters/groups.

AIM groupvar /CONTINUOUS scalevar /PLOT ERRORBAR.

will plot the scalevar's means + confidence intervals by the groups of groupvar.

The confidence intevals plotted are the "simultaneous" CIs, they are wider than the usual, individual CIs, because for each group they include the information that there are several groups. But what is the specific formula these simultaneous CIs are computed by? and what is the idea behind it? I could not find any explanation in Algorithms (AIM chapter or "Cluster Evaluation" chapter) and in CSR (AIM command). Please, give the formula here and also add it to the Algorithms document (AIM command).

Individual confidence interval is the percentage of confidence intervals that will include the true population parameter or true difference between factor levels if the study were repeated multiple times. Simultaneous confidence level is the percentage of times that a group of confidence intervals will include  all the true population parameters or true differences between factor levels if the study were repeated multiple times. The simultaneous confidence level is based on both the individual confidence level and the number of confidence intervals. For a single comparison, the simultaneous confidence level is equal to the individual confidence level. However, each additional confidence interval causes the simultaneous confidence level to decrease in a cumulative way. The expressions for calculation of simultaneous confidence intervals in case of small and large samples are attached.

Tukey's method, Fisher's least significant difference (LSD), Hsu's multiple comparisons with the best (MCB), and Bonferroni confidence intervals are methods for calculating and controlling the individual and simultaneous confidence levels. Bonferroni method is a method for controlling the simultaneous confidence level for an entire set of confidence intervals. It is important to consider the simultaneous confidence level when we examine multiple confidence intervals because our chances that at least one of the confidence intervals does not contain the population parameter is greater for a set of intervals than for any single interval. To counter this higher error rate, the Bonferroni method adjusts the confidence level for each individual interval so that the resulting simultaneous confidence level is equal to the value we specify. This conservative method ensures that the overall confidence level is at least 1-a where a is the significance level. To obtain an overall confidence level of 1 - a for the joint interval estimates, SPSS constructs each interval with a confidence level of (1 - a/k), where k is the number of intervals. In the Bonferroni intervals, SPSS uses 99% confidence intervals (1.00 - 0.05/5 = 0.99) to achieve the 95% simultaneous confidence level.

AIM command in SPSS Statistics explores cluster (or other groups) profiles and assesses feature importance in differentiating clusters/groups.

AIM groupvar /CONTINUOUS scalevar /PLOT ERRORBAR.

will plot the scalevar's means + confidence intervals by the groups of groupvar.

The confidence intevals plotted are the "simultaneous" CIs, they are wider than the usual, individual CIs, because for each group they include the information that there are several groups. But what is the specific formula these simultaneous CIs are computed by? and what is the idea behind it? I could not find any explanation in Algorithms (AIM chapter or "Cluster Evaluation" chapter) and in CSR (AIM command). Please, give the formula here and also add it to the Algorithms document (AIM command).

Thank you for the reply. So, it sounds that you are confirming my supposition (see above) that AIM command uses the Bonferroni corrected CI on its plot. Right?

Individual confidence interval is the percentage of confidence intervals that will include the true population parameter or true difference between factor levels if the study were repeated multiple times. Simultaneous confidence level is the percentage of times that a group of confidence intervals will include  all the true population parameters or true differences between factor levels if the study were repeated multiple times. The simultaneous confidence level is based on both the individual confidence level and the number of confidence intervals. For a single comparison, the simultaneous confidence level is equal to the individual confidence level. However, each additional confidence interval causes the simultaneous confidence level to decrease in a cumulative way. The expressions for calculation of simultaneous confidence intervals in case of small and large samples are attached.

Tukey's method, Fisher's least significant difference (LSD), Hsu's multiple comparisons with the best (MCB), and Bonferroni confidence intervals are methods for calculating and controlling the individual and simultaneous confidence levels. Bonferroni method is a method for controlling the simultaneous confidence level for an entire set of confidence intervals. It is important to consider the simultaneous confidence level when we examine multiple confidence intervals because our chances that at least one of the confidence intervals does not contain the population parameter is greater for a set of intervals than for any single interval. To counter this higher error rate, the Bonferroni method adjusts the confidence level for each individual interval so that the resulting simultaneous confidence level is equal to the value we specify. This conservative method ensures that the overall confidence level is at least 1-a where a is the significance level. To obtain an overall confidence level of 1 - a for the joint interval estimates, SPSS constructs each interval with a confidence level of (1 - a/k), where k is the number of intervals. In the Bonferroni intervals, SPSS uses 99% confidence intervals (1.00 - 0.05/5 = 0.99) to achieve the 95% simultaneous confidence level.

AIM command in SPSS Statistics explores cluster (or other groups) profiles and assesses feature importance in differentiating clusters/groups.

AIM groupvar /CONTINUOUS scalevar /PLOT ERRORBAR.

will plot the scalevar's means + confidence intervals by the groups of groupvar.

The confidence intevals plotted are the "simultaneous" CIs, they are wider than the usual, individual CIs, because for each group they include the information that there are several groups. But what is the specific formula these simultaneous CIs are computed by? and what is the idea behind it? I could not find any explanation in Algorithms (AIM chapter or "Cluster Evaluation" chapter) and in CSR (AIM command). Please, give the formula here and also add it to the Algorithms document (AIM command).