# Statistics for basis functions

Dear Colleagues,

Hi. I hypothesize that the answers to all the questions below are "yes" but would very much appreciate a check of my thoughts.

Sincerely,

Dante

-1-
In multiple regression/correlation using Type III sum of squares, are the statistics associated with individual predictor variables in the model always marginal/partial statistics?
-2-
When using basis functions in a single-subject, event-related functional MRI analysis with one stimulus and eight inflection points, are the statistics for each inflection point marginal/partial statistics?
-3-
In Question 2, do the statistics for each inflection point test the significance of the fit between the observed functional MRI signal and the predicted signal given by the inflection point's basis function?
-4-
In Question 2, if a second stimulus is added to the model, are the statistics for all 16 inflection points marginal/partial statistics?
-5-
In the -gltsym option to 3dDeconvolve, if only a single row is provided with a single stimulus class (e.g., +ToolMovie), then does the contrast test if that one stimulus class has a nonzero integrated hemodynamic response function?
-6-
In Question 5, can the contrast be considered analogous to a "main effect" where it is performed while collapsing across all other stimuli in the model?

Hi Dante,

-1-
In multiple regression/correlation using Type III sum of squares, are the statistics associated with individual predictor variables in the model always marginal/partial statistics?
-2-
When using basis functions in a single-subject, event-related functional MRI analysis with one stimulus and eight inflection points, are the statistics for each inflection point marginal/partial statistics?

All effect estimates in a regression model are assessed as marginal.

-3-
In Question 2, do the statistics for each inflection point test the significance of the fit between the observed functional MRI signal and the predicted signal given by the inflection point's basis function?

Between two models: the full model and the model without the basis function.

-4-
In Question 2, if a second stimulus is added to the model, are the statistics for all 16 inflection points marginal/partial statistics?

Still marginal.

-5-
In the -gltsym option to 3dDeconvolve, if only a single row is provided with a single stimulus class (e.g., +ToolMovie), then does the contrast test if that one stimulus class has a nonzero integrated hemodynamic response function?

It assesses the area under the fitted curve, which is not optimal. With eight bases, I recommend using a multi-row specification with double brackets to assess the overall effect of each HDR:

``````+ToolMovie[[0..7]]
``````

-6-
In Question 5, can the contrast be considered analogous to a "main effect" where it is performed while collapsing across all other stimuli in the model?

Instead of collapsing, do something like

``````+ToolMovie[[0..7]] -ToolImage[[0..7]]
``````

Gang

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