Permutation Inference for Canonical Correlation Analysis

Canonical correlation analysis (CCA) has become a key tool for population neuroimaging, allowing investigation of associations between many imaging and non-imaging measurements. As other variables are often a source of variability not of direct interest, previous work has used CCA on residuals from a model that removes these effects, then proceeded directly to permutation inference. We show that such a simple permutation test leads to inflated error rates. The reason is that residualisation introduces dependencies among the observations that violate the exchangeability assumption. Even in the absence of nuisance variables, however, a simple permutation test for CCA also leads to excess error rates for all canonical correlations other than the first. The reason is that a simple permutation scheme does not ignore the variability already explained by previous canonical variables. Here we propose solutions for both problems: in the case of nuisance variables, we show that transforming the residuals to a lower dimensional basis where exchangeability holds results in a valid permutation test; for more general cases, with or without nuisance variables, we propose estimating the canonical correlations in a stepwise manner, removing at each iteration the variance already explained, while dealing with different number of variables in both sides. We also discuss how to address the multiplicity of tests, proposing an admissible test that is not conservative, and provide a complete algorithm for permutation inference for CCA.Comment: 49 pages, 2 figures, 10 tables, 3 algorithms, 119 reference

Results of investigations conducted in the LaRC 8-foot transonic pressure tunnel using the 0.010-scale 72-OTS model of the space shuttle integrated vehicle (IA93), volume 2

Test procedures, history, and plotted coefficient data are presented for an aero-loads investigation on the updated configuration-5 space shuttle launch vehicle at Mach numbers from 0.600 to 1.205. Six-component vehicle forces and moments, base and sting-cavity pressures, elevon hinge moments, wing-root bending and torsion moments, and normal shear force data were obtained. Full simulation of updated vehicle protuberances and attach hardware was employed

Results of investigations conducted in the LaRC 4-foot unitary plan wind tunnel leg no. 1 using the 0.010-scale 72-OTS model of the space shuttle integrated vehicle (IA94A)

Aero-loads investigations were conducted on the updated configuration-5 space shuttle launch vehicle at Mach numbers 2.50, 3.50, and 4.50. Six-component vehicle forces and moments, base and sting-cavity pressures, elevon hinge moments, wing-root bending and torsion moments, and normal shear force data were obtained. Full simulation of updated vehicle protuberances and attach hardware was employed. Various elevon deflection angles were tested, with two different forward orbiter-to-external-tank attach-strut configurations. The entire vehicle model 72-OTS was supported by means of a balance mounted in the orbiter through its base and suspended from an appropriate sting for the specific tunnel

Results of investigations (OA20C) on an 0.015-scale configuration 140A/B space shuttle vehicle orbiter model (49-0) in the NASA/Langley Research Center Unitary Plan Wind Tunnel

Data obtained from the wind tunnel tests of a scale model of the space shuttle orbiter configuration 140 A/B are presented. The test was conducted at Mach numbers of 2.5, 3.9, and 4.6 with Reynolds numbers from 1.25 million per foot to 5.0 million per foot. Various control surface settings were used ranging from an angle of attack range from minus 4 to plus 42 degrees at zero angle of yaw. Longitudinal stability and control characteristics of the space shuttle configuration were analyzed

Results of flow-visualization investigations on a 0.015-scale modified configuration 140A/B space shuttle vehicle orbiter (model 36-0) in the Langley Research Center 8-foot transonic pressure tunnel (OA102)

The results are presented of a flow-visualization wind tunnel test of a 0.015-scale model of the Modified Configuration 140A/B Space Shuttle Vehicle Orbiter. Separation zones, flow-recirculation regions, and potential venting and contaminant-ingestion problem areas were studied by means of photographic (video tape) analysis of model-mounted tufts. The model was tested at Mach numbers of 0.60, 0.90, 1.05, and 1.20, at Reynolds numbers of 3.17, 3.98, 4.16, and 4.23, respectively. Model angle-of-attack was varied from 0 deg to 20 deg at 0 deg sideslip-angle. Three control-surface deflection combinations were tested

Results of a jet plume effects test on Rockwell International integrated space shuttle vehicle using a vehicle 5 configuration 0.02-scale model (88-OTS) in the 11 by 11 foot leg of the NASA/Ames Research Center unitary plan wind tunnel (IA19), volume 1

Results are presented of jet plume effects test IA19 using a vehicle 5 configuration integrated space shuttle vehicle 0.02-scale model in the NASA/Ames Research Center 11 x 11-foot leg of the unitary plan wind tunnel. The jet plume power effects on the integrated vehicle static pressure distribution were determined along with elevon, main propulsion system nozzle, and solid rocket booster nozzle effectiveness and elevon hinge moments

Investigations on an 0.030-scale space shuttle vehicle configuration 140A/B orbiter model in the Ames Research Center 9 by 7-foot supersonic wind tunnel (OA53B)

A wind tunnel test of an 0.030-scale space shuttle vehicle orbiter configuration 140A/B model was conducted in the Ames Research Center 9- by 7-foot supersonic wind tunnel. This part of test series OA53 was conducted at Mach numbers of 1.60 and 2.00 and at Reynolds numbers ranging from 1.0 million per foot to 4.0 million per foot. The objective was to establish and verify longitudinal and lateral-directional aerodynamic performance, stability, and control characteristics for the configuration 140A/B SSV orbiter. Reynolds number studies were performed on certain nominal control-setting configurations, and examinations were made of the incremental effects of an alternate wing leading-edge configuration and of a sealed elevon-split construction. Six-component force and moment data, base and cavity pressures, bodyflap, elevon, speedbrake, and rudder hinge moments, and vertical tail forces and moments were measured for the orbiter

Results of investigations (OA20A) on a 0.015-scale 140A/B configuration space shuttle vehicle orbiter model in the NASA/Langley Research Center unitary plan wind tunnel

Data obtained from a wind tunnel test of a 0.015-scale 140A/B configuration SSV orbiter model are presented. This test was conducted with runs at Mach numbers of 2.5, 3.9, and 4.6 for a constant Reynolds number of 2.5 x 1,000,000/foot. Only one model configuration, the complete 140A/B orbiter vehicle, was investigated; various control-surface settings were run through angles-of-attack from -4 to +42 degrees at 0 and +3 degrees of yaw and through angles-of-sideslip from -4 to +6 degrees at 0, +10, +20, and +30 degrees pitch. The purpose of this test was to establish and verify longitudinal and lateral-directional stability and control characteristics for the updated SSV configuration

Results of an investigation to determine local flow characteristics at the air data probe locations using an 0.030-scale model (45-0) of the space shuttle vehicle orbiter configuration 140A/B (modified) in the NASA Ames Research Center unitary plan wind tunnel (OA161, A, B, C), volume 2

For abstract, see N76-32235

Investigations of the 0.020-scale 88-OTS Integrated Space Shuttle Vehicle Jet-Plume Model in the NASA/Ames Research Center 11 by 11-Foot Unitary Plan Wind Tunnel (IA80)

Tabulated pressure data are presented for the external tank and the external tank base. For abstract, see N76-33263