Linear Regression with Dummy Interaction

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FE 2021-7-21

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评论： Peter Perkins 2021-7-28

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Hi,

I am looking to estimate a linear regression in the following manner:

I want to estimate

(a constant), the μ, and the ζ. I have coded both dummies as NxN matrixes containing 1 or 0 in the diagonal depending on the specif year, P(t),P(t-1) and A are vectors of length N.

I have tried to use fitlm by creating a table with all imputs.

fit2 = fitlm(tbl,'p~ d1+d2*pre_p+prod');

My error is the following:

"Predictor variables must be numeric vectors, numeric matrices, or categorical vectors."

I know that the issue lies in the coding of the dummy variable. My question is about implementation.

Thanks !

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Ive J 2021-7-23

编辑：Ive J 2021-7-23

在 MATLAB Online 中打开

Now it makes sense why MATLAB threw that error: d1 and d2 are not categorical vectors. This example may help you:

load carbig.mat
tbl = table(Acceleration, Weight, cyl4, MPG, 'VariableNames', {'acceleration', 'weight', 'cylinder', 'MPG'});
% do some fitting
mdl1 = fitlm(tbl) % equivalent to mpg ~ acceleration + weight + cylinder (char vector)
mdl1 = 
Linear regression model:
    MPG ~ 1 + acceleration + weight + cylinder

Estimated Coefficients:
                      Estimate         SE        tStat       pValue  
                     __________    __________    ______    __________

    (Intercept)          34.885        2.1643    16.118    2.9776e-45
    acceleration        0.20931      0.083609    2.5034      0.012704
    weight           -0.0055827    0.00042167    -13.24    2.3433e-33
    cylinder_Four        3.8128       0.70242    5.4281    9.9757e-08


Number of observations: 398, Error degrees of freedom: 394
Root Mean Squared Error: 4.16
R-squared: 0.719,  Adjusted R-Squared: 0.717
F-statistic vs. constant model: 336, p-value = 2.8e-108
mdl2 = fitlm(tbl, 'CategoricalVars', 'cylinder') % fitlm automatically treated cylinder as categorical variable, so mdl1 and mdl2 are the same!
mdl2 = 
Linear regression model:
    MPG ~ 1 + acceleration + weight + cylinder

Estimated Coefficients:
                      Estimate         SE        tStat       pValue  
                     __________    __________    ______    __________

    (Intercept)          34.885        2.1643    16.118    2.9776e-45
    acceleration        0.20931      0.083609    2.5034      0.012704
    weight           -0.0055827    0.00042167    -13.24    2.3433e-33
    cylinder_Four        3.8128       0.70242    5.4281    9.9757e-08


Number of observations: 398, Error degrees of freedom: 394
Root Mean Squared Error: 4.16
R-squared: 0.719,  Adjusted R-Squared: 0.717
F-statistic vs. constant model: 336, p-value = 2.8e-108
mdl3 = fitlm(tbl, 'MPG~acceleration + weight*cylinder') % add interaction term between a categorical and a numerical predictor
mdl3 = 
Linear regression model:
    MPG ~ 1 + acceleration + weight*cylinder

Estimated Coefficients:
                             Estimate         SE         tStat       pValue  
                            __________    __________    _______    __________

    (Intercept)                 29.889        2.3491     12.724    2.6898e-31
    acceleration               0.26218      0.082104     3.1932     0.0015202
    weight                  -0.0044292    0.00047548    -9.3153    8.8175e-19
    cylinder_Four               15.775        2.5833     6.1064     2.449e-09
    weight:cylinder_Four    -0.0045521    0.00094803    -4.8016    2.2411e-06


Number of observations: 398, Error degrees of freedom: 393
Root Mean Squared Error: 4.05
R-squared: 0.735,  Adjusted R-Squared: 0.732
F-statistic vs. constant model: 272, p-value = 7.78e-112
% can I also convert a numeric vector to a categorical one? YES!
tbl.Model_Year = categorical(Model_Year);
mdl4 = fitlm(tbl, 'MPG~acceleration + weight + Model_Year*cylinder')
mdl4 = 
Linear regression model:
    MPG ~ 1 + acceleration + weight + cylinder*Model_Year

Estimated Coefficients:
                                    Estimate         SE          tStat        pValue  
                                   __________    __________    _________    __________

    (Intercept)                        33.117        1.6691       19.841    3.4779e-60
    acceleration                      0.11081      0.065727       1.6859      0.092663
    weight                         -0.0051584    0.00032653      -15.798    2.4833e-43
    cylinder_Four                      2.2221        1.4003       1.5869       0.11339
    Model_Year_71                     0.89635        1.0156      0.88261       0.37802
    Model_Year_72                     0.55101        1.0413      0.52915       0.59702
    Model_Year_73                     0.13321       0.85754      0.15534       0.87664
    Model_Year_74                     0.97798        1.1139      0.87798       0.38052
    Model_Year_75                     0.78487       0.99652      0.78761       0.43143
    Model_Year_76                      1.6973       0.96736       1.7546       0.08016
    Model_Year_77                      2.4339         1.048       2.3223      0.020757
    Model_Year_78                      1.6757       0.97294       1.7223      0.085848
    Model_Year_79                      3.9992         1.003       3.9874    8.0515e-05
    Model_Year_80                      8.1649        1.6708       4.8867      1.53e-06
    Model_Year_81                      5.3128        1.2778       4.1578    3.9969e-05
    Model_Year_82                      8.5627        1.8863       4.5395     7.636e-06
    cylinder_Four:Model_Year_71     -0.045407        1.7406    -0.026086        0.9792
    cylinder_Four:Model_Year_72       -2.0781         1.737      -1.1964       0.23232
    cylinder_Four:Model_Year_73       -2.5828        1.6884      -1.5297       0.12694
    cylinder_Four:Model_Year_74       0.76411        1.7716      0.43132       0.66649
    cylinder_Four:Model_Year_75       0.21242        1.7482      0.12151       0.90335
    cylinder_Four:Model_Year_76      -0.24002        1.6788     -0.14297       0.88639
    cylinder_Four:Model_Year_77       0.92909        1.7456      0.53224       0.59488
    cylinder_Four:Model_Year_78        2.6054        1.6649       1.5649       0.11845
    cylinder_Four:Model_Year_79        2.5763          1.75       1.4722       0.14181
    cylinder_Four:Model_Year_80        1.3828         2.107      0.65631       0.51203
    cylinder_Four:Model_Year_81        2.0758        1.8299       1.1344       0.25735
    cylinder_Four:Model_Year_82       -1.2888        2.2756     -0.56635        0.5715


Number of observations: 398, Error degrees of freedom: 370
Root Mean Squared Error: 3.01
R-squared: 0.861,  Adjusted R-Squared: 0.851
F-statistic vs. constant model: 85.2, p-value = 5.27e-141

FE 2021-7-27

Hi,

Thank you for all the contributions and examples. I do believe I know why it does not work, what I don t understand is how to define the dummy such that it fits what I want to do.

I need two dummies:

the first is equal to one from 2000 Q1 - 2019 Q4 and else 0

the second is equal one from 1990 Q1 - 1999 Q4 and else 0

I don t see how fitlm "takes care" without proper definition.... so I am confused about implmentation.

Now what I did in the mean time, although extremly unelegant is code dummy 1 (equal to one from 2000 Q1 - 2019 Q4 and else 0) as a vector variable, and the other dummy 2 (equal one from 1990 Q1 - 1999 Q4 and else 0 ) I multiplied with my vector p(t-1) and then run my regression...

There should be a more straight forward way no?

Peter Perkins 2021-7-28

If you use a categorical variable as a predictor in your model, fitlm will create dummy variables internally. I'm suire there are examples in the doc. You don't need to create dummy vars unless you want some non-standard coding. Maybe that's what you want. If so, creatre LOGICAL or NUMERIC dummy variables yourself. Based on the limited information you have provided, it appears that maybe you have been creating categorrical dummy variables.

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