How to make a contrast matrix to test interaction effects, for fitlme?

I have 3 factors with each having multiple levels. Factor color has 3 levels, order has 4 levels and condition has 5 levels. I want to look at the main and interaction effect on the outcome variable, individual_correction_error. I have subjects as the random effect.

I have excluded condition_3 as there was no data there.

I would like to use coeftest to do post hoc analysis on this data. How do I go about building the contrast matrix for sepcifically testing the interaction between condition and order?

This is the output of fitlme on the model ('individual_correction_error ~ color*condition*order+(1|subject)')

lm_full_condition =

Linear mixed-effects model fit by ML

Model information:

Number of observations 2286

Fixed effects coefficients 48

Random effects coefficients 45

Covariance parameters 2

Formula:

individual_correction_error ~ 1 + color*condition + color*order + condition*order + color:condition:order + (1 | subject)

Model fit statistics:

AIC BIC LogLikelihood Deviance

12030 12316 -5964.9 11930

Fixed effects coefficients (95% CIs):

Name Estimate SE tStat DF pValue Lower Upper

{'(Intercept)' } -0.15933 0.74743 -0.21317 2238 0.83121 -1.6251 1.3064

{'color_blue' } -0.1484 0.098592 -1.5052 2238 0.13241 -0.34174 0.044939

{'color_green' } 0.13717 0.098592 1.3912 2238 0.16429 -0.056176 0.33051

{'condition_4' } -2.8125 0.15171 -18.538 2238 1.7385e-71 -3.11 -2.515

{'condition_2' } -0.13007 0.11213 -1.16 2238 0.24619 -0.34996 0.089826

{'condition_1' } 3.0123 0.16372 18.398 2238 1.6508e-70 2.6912 3.3333

{'order_[0 1 2 4 3]' } 1.1165 0.8071 1.3834 2238 0.16669 -0.46624 2.6993

{'order_[0 2 3 1 4]' } 0.14848 1.3039 0.11387 2238 0.90935 -2.4085 2.7055

{'order_[0 3 4 2 1]' } -2.3417 1.2672 -1.8478 2238 0.064757 -4.8267 0.14343

{'color_blue:condition_4' } 0.27389 0.18359 1.4918 2238 0.13588 -0.086139 0.63392

{'color_green:condition_4' } -0.34359 0.18359 -1.8715 2238 0.061407 -0.70362 0.016437

{'color_blue:condition_2' } -0.12677 0.15211 -0.83338 2238 0.40472 -0.42507 0.17153

{'color_green:condition_2' } 0.075611 0.15211 0.49707 2238 0.61919 -0.22269 0.37391

{'color_blue:condition_1' } -0.25319 0.19023 -1.331 2238 0.18332 -0.62623 0.11985

{'color_green:condition_1' } 0.14719 0.19023 0.77377 2238 0.43915 -0.22585 0.52023

{'color_blue:order_[0 1 2 4 3]' } 0.30762 0.17161 1.7925 2238 0.073182 -0.028914 0.64416

{'color_green:order_[0 1 2 4 3]' } -0.30302 0.17161 -1.7657 2238 0.077581 -0.63956 0.033519

{'color_blue:order_[0 2 3 1 4]' } 0.10408 0.17381 0.59878 2238 0.54938 -0.23677 0.44492

{'color_green:order_[0 2 3 1 4]' } -0.013282 0.17381 -0.076417 2238 0.93909 -0.35413 0.32757

{'color_blue:order_[0 3 4 2 1]' } -0.33717 0.1713 -1.9682 2238 0.049165 -0.6731 -0.0012345

{'color_green:order_[0 3 4 2 1]' } 0.26726 0.1713 1.5601 2238 0.11887 -0.068678 0.60319

{'condition_4:order_[0 1 2 4 3]' } 0.11191 0.2537 0.44112 2238 0.65917 -0.3856 0.60943

{'condition_2:order_[0 1 2 4 3]' } 0.64807 0.20125 3.2203 2238 0.001299 0.25342 1.0427

{'condition_1:order_[0 1 2 4 3]' } -0.38955 0.2858 -1.363 2238 0.17301 -0.95002 0.17091

{'condition_4:order_[0 2 3 1 4]' } 0.78129 0.29921 2.6112 2238 0.0090828 0.19454 1.368

{'condition_2:order_[0 2 3 1 4]' } -0.72327 0.1926 -3.7553 2238 0.00017757 -1.101 -0.34557

{'condition_1:order_[0 2 3 1 4]' } -0.50564 0.25323 -1.9968 2238 0.045969 -1.0022 -0.0090558

{'condition_4:order_[0 3 4 2 1]' } -1.2315 0.24498 -5.0268 2238 5.3815e-07 -1.7119 -0.75105

{'condition_2:order_[0 3 4 2 1]' } -1.1713 0.19561 -5.988 2238 2.4683e-09 -1.5549 -0.78773

{'condition_1:order_[0 3 4 2 1]' } 2.3455 0.29693 7.8989 2238 4.3708e-15 1.7632 2.9278

{'color_blue:condition_4:order_[0 1 2 4 3]' } 0.12839 0.3146 0.4081 2238 0.68324 -0.48854 0.74532

{'color_green:condition_4:order_[0 1 2 4 3]'} 0.14677 0.3146 0.46654 2238 0.64088 -0.47016 0.7637

{'color_blue:condition_2:order_[0 1 2 4 3]' } -0.10329 0.2706 -0.3817 2238 0.70272 -0.63394 0.42737

{'color_green:condition_2:order_[0 1 2 4 3]'} 0.14738 0.2706 0.54464 2238 0.58606 -0.38328 0.67804

{'color_blue:condition_1:order_[0 1 2 4 3]' } 0.17675 0.3325 0.53158 2238 0.59507 -0.47529 0.82879

{'color_green:condition_1:order_[0 1 2 4 3]'} -0.22094 0.3325 -0.66448 2238 0.50645 -0.87298 0.4311

{'color_blue:condition_4:order_[0 2 3 1 4]' } -0.033804 0.34999 -0.096585 2238 0.92306 -0.72015 0.65254

{'color_green:condition_4:order_[0 2 3 1 4]'} -0.20315 0.34999 -0.58045 2238 0.56167 -0.8895 0.48319

{'color_blue:condition_2:order_[0 2 3 1 4]' } 0.2268 0.26636 0.85149 2238 0.39459 -0.29554 0.74914

{'color_green:condition_2:order_[0 2 3 1 4]'} -0.13989 0.26636 -0.52518 2238 0.59951 -0.66223 0.38245

{'color_blue:condition_1:order_[0 2 3 1 4]' } 0.30113 0.30137 0.9992 2238 0.3178 -0.28987 0.89213

{'color_green:condition_1:order_[0 2 3 1 4]'} -0.089843 0.30137 -0.29811 2238 0.76565 -0.68084 0.50116

{'color_blue:condition_4:order_[0 3 4 2 1]' } 0.36974 0.30391 1.2166 2238 0.22388 -0.22623 0.96571

{'color_green:condition_4:order_[0 3 4 2 1]'} -0.021389 0.30391 -0.07038 2238 0.9439 -0.61736 0.57458

{'color_blue:condition_2:order_[0 3 4 2 1]' } -0.13751 0.26 -0.52888 2238 0.59694 -0.64738 0.37236

{'color_green:condition_2:order_[0 3 4 2 1]'} -0.11538 0.26 -0.44375 2238 0.65726 -0.62524 0.39449

{'color_blue:condition_1:order_[0 3 4 2 1]' } -0.73679 0.35229 -2.0914 2238 0.036604 -1.4276 -0.045935

{'color_green:condition_1:order_[0 3 4 2 1]'} 0.48379 0.35229 1.3732 2238 0.16981 -0.20707 1.1746

Random effects covariance parameters (95% CIs):

Group: subject (45 Levels)

Name1 Name2 Type Estimate Lower Upper

{'(Intercept)'} {'(Intercept)'} {'std'} 4.9857 4.0418 6.1499

Group: Error

Name Estimate Lower Upper

{'Res Std'} 3.1361 3.0456 3.2293

Answer 1

[Shivansh]

Hi MM,

I understand that you want to create a contrast matrix to test the interaction between two factors using the coefTest function in MATLAB.

I assume from the output provided by you that you have a mixed effect model ‘lme’.

You can follow the below steps to test the interaction between “condition” and “order” factors.

1. Define the contrast matrix for the interaction term you want to test. In this case, you want to test the interaction between "condition" and "order," so create a contrast matrix to capture this interaction. Here is an example code to create a contrast matrix.

% Define the levels for the factors
numColorLevels = 3;
numOrderLevels = 4;
numConditionLevels = 5;

% Create the contrast matrix for the interaction between condition and order
% This will compare all combinations of condition and order levels
interactionContrast = zeros(numColorLevels * numOrderLevels, numConditionLevels * numOrderLevels);

% Fill in the contrast matrix
for i = 1:numColorLevels
    for j = 1:numOrderLevels
        interactionContrast((i - 1) * numOrderLevels + j, (i - 1) *numConditionLevels + 1:j * numConditionLevels) = 1;
    end
end

2. Use the ‘coefTest’ function to perform the hypothesis test for the interaction effect. Pass the mixed-effects model (lme) and the contrast matrix you have defined as the arguements to ‘coefTest’ function.

 interactionTest = coefTest(lme, interactionContrast);

To learn more about the ‘coefTest’ function, please refer to the following documentation link: https://in.mathworks.com/help/stats/linearmodel.coeftest.html.

3. The interactionTest object will contain the test statistics and p-values for the interaction effect between the factors. You can then examine the interactionTest object to determine if the interaction effect is statistically significant.

Further, kindly adjust the code snippets according to your requirements to get the appropriate results.

I hope it resolves your issue!