Why is my Mixed ANOVA including the intercept as an interaction term?

Hi there,

I have been getting different outputs from Matlab to JASP and SPSS, both of which agree that Matlab is wrong, which I think is due to the intercept being included as an interaction term in the model spec.

I have run a 2b*6w*2w Mixed ANOVA in Matlab. (Between-2=Consciousness, Within-6 = Conguency, Within-2 =Target) However I am getting the intercept as an interaction term in my ranova table:

Matlab Output

The factors Congruency and Target should be reported only as a main effects, not as an interaction with the intercept.

I'm including a JASP output so to compare the difference between the two softwares.

Could you take a look at my code, I think I've done something wrong in the Wilkinson notation of the model specification, and tell me how I stop it using the intercept as an interaction term.

OverallDataTable=readtable('Data.xlsx')

WithinDesign=table(categorical({'Related Hand','Related Foot','Unrelated Hand','Unrelated Foot', ...
    'Neutral Hand','Neutral Foot','Related Hand','Related Foot','Unrelated Hand','Unrelated Foot', ...
    'Neutral Hand','Neutral Foot'}'),categorical({'BP','BP','BP','BP','BP','BP','O','O','O','O','O','O'}'), ...
    'VariableNames',{'Congruency','Target'});

OverallMixedANOVA=fitrm(OverallDataTable,'BP_RH_Con-O_NF_Sub~Consciousness',WithinDesign=WithinDesign);

OverallMixedANOVATable=ranova(OverallMixedANOVA,"WithinModel",'Congruency*Target')

Thanks for any and all advice

Dan

Answer 1

[Jeff Miller]

I think you need

OverallDataTable.Consciousness = categorical(OverallDataTable.Consciousness);

[Dan]

Thank you so much!

I've been stuck on this for a week! Typically, its one of those simple things that I completely overlooked!

Thanks again!

[Adam Danz]

Thanks @Jeff Miller. Good find.

The doc page for fitrm states that "fitrm treats the variables used in model terms as categorical if they are categorical (nominal or ordinal), logical, character arrays, string arrays, or cell arrays of character vectors". I am just now realizing that the Consciousness variable is double, not logical.

Another solution would be to set Consciousness to logical.

Answer 2

[Adam Danz]

You can remove the interaction term by including "-1" in the model spec (doc). I also included terms for Congruency and Target in the WithinModel so the table rows match the JASP version.

format longg

% No change here
OverallDataTable=readtable('Data.xlsx')

OverallDataTable = 195x14 table
    ID       BP_RH_Con           BP_RF_Con           BP_UH_Con           BP_UF_Con           BP_NH_Con           BP_NF_Con            O_RH_Sub            O_RF_Sub            O_UH_Sub            O_UF_Sub            O_NH_Sub            O_NF_Sub        Consciousness
    __    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    _____________

     1    569.066666666667    654.315789473684    635.026315789474               649.6    626.857142857143    596.380952380952    445.022222222222    505.619047619048    530.883720930233    509.276595744681    568.756097560976    533.609756097561          0      
     2    516.389130434783              510.76    504.940425531915     511.80652173913    491.534782608696    526.611111111111    468.991489361702    490.810869565217              508.45    505.704347826087    551.667441860465    551.068181818182          0      
     3    623.022222222222    627.739130434783    607.152173913043    654.431818181818    621.477272727273    638.767441860465    615.217391304348    594.382978723404    599.826086956522    610.702127659574    596.282608695652    622.531914893617          0      
     4    580.157142857143    558.366666666667    531.086046511628    517.976086956522    544.635555555555    535.739534883721    444.551063829787    473.338095238095    481.334782608696    493.012765957447    531.772093023256    562.148780487805          0      
     6    583.673913043478    551.702127659574    604.402272727273            558.8625    598.448888888889    583.520454545455    522.332608695652    557.708510638298    561.627272727273    524.172340425532    510.435555555555    517.533333333333          0      
     7    564.980952352381    561.772727295455    568.049999890476    627.110810659459    529.464285785714    567.121428557143    501.961363586364        701.47142855    595.478378335135      515.5000000625    833.782142807142         720.8093749          0      
     8     520.95652173913    459.520833333333    494.702127659574    462.063829787234    522.155555555556    483.957446808511    424.666666666667    457.195652173913    461.173913043478    442.595744680851    479.571428571429    476.777777777778          0      
     9    646.193333328889    679.317777784444    659.010869565217    669.291489378723    694.668888893333    691.336956530435    744.278723404255    665.540425542553    680.986956530435    696.097826073913    686.900000004545    682.380000008889          0      
    10    584.834210536842    520.789130428261    564.992857147619    506.754347821739    546.765116269767    555.607142840476    465.568085108511    566.152380957143    565.964102582051    489.133333335556    595.126315797368    514.640909088636          0      
    11     575.91914893617    578.030434782609     574.26170212766    574.474468085106    563.306521739131    552.976595744681    565.846808510638    528.321276595745    510.989130434783    482.934042553191    520.660416666667    505.821739130435          0      
    12     487.04347826087    464.979166666667    503.104166666667    469.765957446808     515.45652173913    472.708333333333    491.239130434783    503.978260869565    491.739130434783    483.595744680851    479.282608695652    480.510638297872          0      
    13    516.035555564445    500.477777733333    581.146341426829     469.20217393913    501.686046523256     478.45869563913    503.948837202326       473.359090925    446.402173913043    472.631111135556        474.56444448    495.333333288889          0      
    14    562.319047607143     559.52619047619    579.676744183721    512.436363643182    580.671739128261    485.810869565217    467.144444431111    479.540909077273        468.99333334    425.502173919565    564.313333324444    536.716279076744          0      
    15    567.531914893617    571.222727272727    555.810869565217    545.786956521739    586.253191489362           559.79375              498.34    509.959574468085    522.108510638298    489.197826086956    519.334042553192              523.15          0      
    16    597.374418604651    597.123404255319    618.056521739131     603.01914893617    592.311111111111    619.293617021277    561.226086956522    531.121739130435              534.04              532.04    583.576086956522    593.095744680851          0      
    17    584.972727272727    635.369230769231    600.997619047619    606.004878048781    571.816279069767    630.952380952381    561.440425531915    491.786956521739               562.3    528.339130434783    548.782222222222    530.697727272727          0      

WithinDesign=table(categorical({'Related Hand','Related Foot','Unrelated Hand','Unrelated Foot', ...
    'Neutral Hand','Neutral Foot','Related Hand','Related Foot','Unrelated Hand','Unrelated Foot', ...
    'Neutral Hand','Neutral Foot'}'),categorical({'BP','BP','BP','BP','BP','BP','O','O','O','O','O','O'}'), ...
    'VariableNames',{'Congruency','Target'})

WithinDesign = 12x2 table
      Congruency      Target
    ______________    ______

    Related Hand        BP  
    Related Foot        BP  
    Unrelated Hand      BP  
    Unrelated Foot      BP  
    Neutral Hand        BP  
    Neutral Foot        BP  
    Related Hand        O   
    Related Foot        O   
    Unrelated Hand      O   
    Unrelated Foot      O   
    Neutral Hand        O   
    Neutral Foot        O   

OverallMixedANOVA=fitrm(OverallDataTable,'BP_RH_Con-O_NF_Sub~Consciousness',WithinDesign=WithinDesign);

%% New WithinModel spec
OverallMixedANOVATable=ranova(OverallMixedANOVA,"WithinModel",'Congruency+Target+Congruency*Target-1')

OverallMixedANOVATable = 9x8 table
                                            SumSq          DF          MeanSq                F                   pValue                 pValueGG                pValueHF                pValueLB      
                                       ________________    ___    ________________    ________________    ____________________    ____________________    ____________________    ____________________

    (Intercept):Congruency             107194.152414621      5    21438.8304829243    8.36833441555248    9.28137173697959e-08    2.98529873459618e-06    2.40828537573198e-06     0.00425684527499502
    Consciousness:Congruency            31382.590285273      5     6276.5180570546    2.44994716985711      0.0322555870821942      0.0497372650079374        0.04841523524835       0.119166973697714
    Error(Congruency)                  2472232.87080552    965    2561.89934798499                                                                                                                    
    (Intercept):Target                 485005.468185154      1    485005.468185154    32.4508255186805    4.50733949742911e-08    4.50733949742911e-08    4.50733949742911e-08    4.50733949742911e-08
    Consciousness:Target               70491.4473790544      1    70491.4473790544    4.71645333817901      0.0310949296797302      0.0310949296797302      0.0310949296797302      0.0310949296797302
    Error(Target)                      2884550.82000456    193    14945.8591710081                                                                                                                    
    (Intercept):Congruency:Target      101277.946737745      5     20255.589347549     9.2725171215368    1.22962731392545e-08    1.11261351901247e-06    8.90177532870524e-07     0.00265102819545689
    Consciousness:Congruency:Target    15566.2107964413      5    3113.24215928826    1.42516669005159       0.212538545990976        0.22908775024349       0.228299426473737       0.234020137725994
    Error(Congruency:Target)           2108019.15641491    965    2184.47580975638                                                                                                                    

Comparing these results with your MATLAB table screen shot does not indicate that removing the main intercept term made a difference for the other terms. I also noticed that data in rows 1, 4, and 7 above do not match the JASP table but the other rows do match. I'm not familiar with JASP but I did see that they may have recently changed thier default ANOVA methods (JASP doc).

Make sure you're using the same alpha value (0.05) in both cases.

Your data does not contain any missing data (NaNs) so that rules out the possibilty that treatment of missing data differs.

I noticed that the JASP table warns against sphericity assumption violations which makes me wonder if any corrections are being applied in JASP (e.g. Greenhouse-Geisser or Huynh-Feldt adjustments).

There's a possibilty that sum of squares is calucated differently but I would expect that to affect all SumSq values, not just select rows.

Lastly, there could be differences in how the overall mixed ANOVA model was specified.

Unfortunately I don't have time to dig further but I would chose one of the rows that have conflicting results and compute the SumSq to make sense of it.

I plotted the data as a sanity check.

M = table2array(OverallDataTable); 
boxchart(M(:,2:end-1))
xline(6.5) % separate conscious and subc. groups

[Dan]

Thanks so much for your work on this.

I had been stuck on this for ages. From the above answer it turns out to be something super simple I should've already known!

Nonetheless, I really appreciate your input, it'll help me methodically debug code in future!

Thanks again