Linear and quadratic terms in 3dMVM

csavage · March 14, 2026, 4:30pm

AFNI version info (afni -ver): AFNI_24.1.19

Hello! I am running a 3dMVM to look at the effect of a task bias score on neural activation, and am also attempting to test the quadratic relationship between bias and activation. The raw bias scores range from 0-1, with numbers close to 0 being a strong negativity bias and numbers close to 1 being a strong positivity bias. For the 3dMVM, I 0-centered and then rescaled the bias scores such that they range from -1 (negativity bias) to +1 (positivity bias), where 0 is no bias. I then squared these scores to get the quadratic term. The output of the 3dMVM have exactly the same results for the linear and the quadratic terms, does anyone know why they would be exactly the same? I have attached my 3dMVM set up as well as the outputs.

code text  # or delete if not needed

Gang · March 16, 2026, 4:15pm

To help troubleshoot, could you clarify a couple of things?

Centering: When you say "0-centered," did you center the scores around the value of 0, or the grand mean of your participants?
The Script: Could you copy and paste the 3dMVM command here? The resolution of the image is too low to read the model specification, the data table, and AFNI GUI interface.

Gang Chen

csavage · March 16, 2026, 6:27pm

I centered the scores around the value of 0. This was so that extreme negative bias would be close to -1 and extreme positive bias would be close to +1. Values at 0 indicate no bias.
Here is the script:

############################################################################################
# GENERAL SETUP
############################################################################################


# Specify the top-most directory associated with the study
set topdir = /data/STUDIES/ISTART/Analyses/fMRI_Analyses

# Specify the directory where subjects' neuroimaging data are located
set subjdata = $topdir/FirstLevel_Images/combined

# Specify the directory where the group analysis results will be written
set results = $topdir/GroupLevelAnalyses/3dMVM

#specify the mask
set mask = $topdir/Masks/ActivationBased/doors/group_mask_monetary_avgFB_thrs90_031626.nii.gz

cd $results

3dMVM 																											                \
 -prefix 3dMVM_monetary_avgFB_bias_0centered_masked_031626											            \
 -jobs 15																										                \
 -qVars "Bias_c,BiasSq"																							        \
 -num_glt 2																							                    \
-gltLabel 1 "LinearBias"    -gltCode 1 'Bias_c : 1'                         \
-gltLabel 2 "QuadraticBias" -gltCode 2 'BiasSq : 1'                         \
-dataTable                                                              \
Subj	Bias_c		BiasSq       InputFile                              \
sub-1001	-0.04167	0.00174	       $subjdata/sub-1001_task-doors_cope5-avgwinloss.nii   \
sub-1002	0.01493	    0.00022	       $subjdata/sub-1002_task-doors_cope5-avgwinloss.nii   \
sub-1006	-0.06667	0.00444	       $subjdata/sub-1006_task-doors_cope5-avgwinloss.nii \
sub-1007	0.34375	    0.11816	        $subjdata/sub-1007_task-doors_cope5-avgwinloss.nii  \
sub-1009	0.00000	    0.00000	        $subjdata/sub-1009_task-doors_cope5-avgwinloss.nii  \
sub-1010	-0.09804	0.00961	        $subjdata/sub-1010_task-doors_cope5-avgwinloss.nii  \
sub-1012	1.00000	    1.00000	        $subjdata/sub-1012_task-doors_cope5-avgwinloss.nii  \
sub-1013	0.17647	    0.03114	        $subjdata/sub-1013_task-doors_cope5-avgwinloss.nii  \
sub-1016	0.09677	    0.00937	        $subjdata/sub-1016_task-doors_cope5-avgwinloss.nii  \
sub-1019	0.36111	    0.13040	        $subjdata/sub-1019_task-doors_cope5-avgwinloss.nii  \
sub-1021	-0.50000	0.25000	        $subjdata/sub-1021_task-doors_cope5-avgwinloss.nii  \
sub-1242	0.71429	    0.51020	        $subjdata/sub-1242_task-doors_cope5-avgwinloss.nii  \
sub-1243	0.58621	    0.34364	        $subjdata/sub-1243_task-doors_cope5-avgwinloss.nii  \
sub-1244	0.76744	    0.58897	        $subjdata/sub-1244_task-doors_cope5-avgwinloss.nii  \
sub-1245	-0.04348	0.00189	        $subjdata/sub-1245_task-doors_cope5-avgwinloss.nii  \
sub-1247	0.56923	    0.32402	        $subjdata/sub-1247_task-doors_cope5-avgwinloss.nii  \
sub-1248	0.29825	    0.08895	        $subjdata/sub-1248_task-doors_cope5-avgwinloss.nii  \
sub-1249	0.70909	    0.50281	        $subjdata/sub-1249_task-doors_cope5-avgwinloss.nii  \
sub-1251	0.08197	    0.00672	        $subjdata/sub-1251_task-doors_cope5-avgwinloss.nii  \
sub-1276	0.27273	    0.07438	        $subjdata/sub-1276_task-doors_cope5-avgwinloss.nii  \
sub-1286	0.00000	    0.00000	        $subjdata/sub-1286_task-doors_cope5-avgwinloss.nii  \
sub-1294	-0.17460	0.03049	        $subjdata/sub-1294_task-doors_cope5-avgwinloss.nii  \
sub-1300	0.29730	    0.08839	        $subjdata/sub-1300_task-doors_cope5-avgwinloss.nii  \
sub-1301	-0.14286	0.02041	        $subjdata/sub-1301_task-doors_cope5-avgwinloss.nii  \
sub-1302	0.00000	    0.00000	        $subjdata/sub-1302_task-doors_cope5-avgwinloss.nii  \
sub-1303	0.32353	    0.10467	        $subjdata/sub-1303_task-doors_cope5-avgwinloss.nii  \
sub-3116	0.27778	    0.07716	        $subjdata/sub-3116_task-doors_cope5-avgwinloss.nii  \
sub-3122	-0.37037	0.13717	        $subjdata/sub-3122_task-doors_cope5-avgwinloss.nii  \
sub-3125	0.32530	    0.10582	        $subjdata/sub-3125_task-doors_cope5-avgwinloss.nii  \
sub-3140	0.29787	    0.08873	        $subjdata/sub-3140_task-doors_cope5-avgwinloss.nii  \
sub-3143	0.59259	    0.35117	        $subjdata/sub-3143_task-doors_cope5-avgwinloss.nii  \
sub-3152	0.50000	    0.25000	        $subjdata/sub-3152_task-doors_cope5-avgwinloss.nii  \
sub-3164	-0.54545	0.29752	        $subjdata/sub-3164_task-doors_cope5-avgwinloss.nii  \
sub-3166	0.11111	    0.01235	        $subjdata/sub-3166_task-doors_cope5-avgwinloss.nii  \
sub-3167	0.29870	    0.08922	        $subjdata/sub-3167_task-doors_cope5-avgwinloss.nii  \
sub-3170	0.60714	    0.36862	        $subjdata/sub-3170_task-doors_cope5-avgwinloss.nii  \
sub-3173	-0.09091	0.00826	        $subjdata/sub-3173_task-doors_cope5-avgwinloss.nii  \
sub-3175	0.24000	    0.05760	        $subjdata/sub-3175_task-doors_cope5-avgwinloss.nii  \
sub-3176	0.44444	    0.19753	        $subjdata/sub-3176_task-doors_cope5-avgwinloss.nii  \
sub-3186	0.68000	    0.46240	        $subjdata/sub-3186_task-doors_cope5-avgwinloss.nii  \
sub-3189	0.00000	    0.00000	        $subjdata/sub-3189_task-doors_cope5-avgwinloss.nii  \
sub-3190	-0.20000	0.04000	        $subjdata/sub-3190_task-doors_cope5-avgwinloss.nii  \
sub-3199	0.23077	    0.05325	        $subjdata/sub-3199_task-doors_cope5-avgwinloss.nii  \
sub-3200	-0.03922	0.00154	        $subjdata/sub-3200_task-doors_cope5-avgwinloss.nii  \
sub-3206	-0.34375	0.11816	        $subjdata/sub-3206_task-doors_cope5-avgwinloss.nii  \
sub-3210	-0.24390	0.05949	        $subjdata/sub-3210_task-doors_cope5-avgwinloss.nii  \
sub-3212	0.13333	    0.01778	        $subjdata/sub-3212_task-doors_cope5-avgwinloss.nii  \
sub-3218	-0.60000	0.36000	        $subjdata/sub-3218_task-doors_cope5-avgwinloss.nii  \
sub-3223	-0.34286	0.11755	        $subjdata/sub-3223_task-doors_cope5-avgwinloss.nii  \
sub-10596	0.30233	    0.09140	        $subjdata/sub-10596_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10606	1.00000	    1.00000	        $subjdata/sub-10606_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10636	-0.07407	0.00549	        $subjdata/sub-10636_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10647	0.26471	    0.07007	        $subjdata/sub-10647_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10656	1.00000	    1.00000	        $subjdata/sub-10656_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10663	-0.28571	0.08163	        $subjdata/sub-10663_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10701	0.33333	    0.11111	        $subjdata/sub-10701_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10723	-0.04167	0.00174	        $subjdata/sub-10723_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10800	0.42857	    0.18367	        $subjdata/sub-10800_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10804	0.27273	    0.07438	        $subjdata/sub-10804_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10806	0.84615	    0.71598	        $subjdata/sub-10806_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10817	0.00000	    0.00000	        $subjdata/sub-10817_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10827	0.00000	    0.00000	        $subjdata/sub-10827_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10831	0.06250	    0.00391	        $subjdata/sub-10831_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10838	0.10204	    0.01041	        $subjdata/sub-10838_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10843	0.41176	    0.16955	        $subjdata/sub-10843_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10857	-0.21875	0.04785	        $subjdata/sub-10857_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10860	0.08696	    0.00756	        $subjdata/sub-10860_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10918	0.31818	    0.10124	        $subjdata/sub-10918_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10950	-0.13433	0.01804	        $subjdata/sub-10950_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10951	-0.01449	0.00021	        $subjdata/sub-10951_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10961	-0.06897	0.00476	        $subjdata/sub-10961_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10969	0.02222 	0.00049	        $subjdata/sub-10969_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10983	0.38462	    0.14793	        $subjdata/sub-10983_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-10998	0.12903	    0.01665	        $subjdata/sub-10998_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-11016	0.03226	    0.00104	        $subjdata/sub-11016_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-11021	0.23077	    0.05325	        $subjdata/sub-11021_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-11030	0.41935	    0.17586	        $subjdata/sub-11030_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-11031	0.40000	    0.16000	        $subjdata/sub-11031_task-doors_cope5-avgwinloss_resampletoISTART.nii  \
sub-11064	0.22807	    0.05202	        $subjdata/sub-11064_task-doors_cope5-avgwinloss_resampletoISTART.nii

Gang · March 16, 2026, 9:07pm

Try the following:

add the line below to your 3dMVM script

-bsVars "Bias_c,BiasSq"  \

add the following to prevent 3dMVM from automatically centering each quantitative variable around its mean

-qVarCenters '0,0'          \

modify the original two lines to the following if you are interested in assessing the linear and quadratic effects

-gltLabel 1 "LinearBias"    -gltCode 1 'Bias_c :'    \
-gltLabel 2 "QuadraticBias" -gltCode 2 'BiasSq :'    \

Gang Chen