[R] Compositional ANOVA With Several Main Effects: Explanation of Results

Rich Shepard rshepard at appl-ecosys.com
Tue May 12 03:34:56 CEST 2015


   The results of compositional ANOVA models with several main effects with
conditional data as the response variable produce 'missing not at random'
(MNAR) results for the same rows in the matrix of output coefficients: the
last, third from last, and fourth from last regardless of the number of
years or which years they are. Why might this happen?

   The model is:
model <- lm(ilr(y) ~ x1 + x2 + x3 + x4)
where x1-x3 are continuous variables and x4 is the discrete varible, year.

   The discrete variable treatment is 'contrasts.' Three data sets are shown
with the *.acomp input matrix and the resulting model coefficients.

set1.acomp:
        Fi         Ga        Gr         Pr        Sh
[1,] 0.06666667 0.6000000 0.06666667 0.2444444 0.02222222
[2,] 0.06122449 0.5714286 0.06122449 0.2653061 0.04081633
[3,] 0.04347826 0.6231884 0.10144928 0.2173913 0.01449275
[4,] 0.04395604 0.5934066 0.06593407 0.2637363 0.03296703
[5,] 0.05000000 0.4333333 0.06666667 0.3666667 0.08333333
[6,] 0.01612903 0.6290323 0.03225806 0.2903226 0.03225806

             Fi           Ga          Gr           Pr          Sh 
(Intercept) 3.115405e-08 0.000279552 2.392303e-11 0.005863277 0.9938571397
x1          6.429247e-02 0.082497400 8.310734e-01 0.021442905 0.0006938677
x2          2.045395e-01 0.197642666 2.021531e-01 0.197459631 0.1982051055
x3          1.736206e-01 0.145594990 5.528400e-01 0.092214496 0.0357298993
x42005      6.161150e-02 0.123183957 2.327678e-02 0.201577707 0.5903500624
x42006              MNAR        MNAR         MNAR        MNAR         MNAR
x42011              MNAR        MNAR         MNAR        MNAR         MNAR
x42012      3.201111e-01 0.071005938 2.128531e-01 0.130202854 0.2658270106
x42013              MNAR        MNAR         MNAR        MNAR         MNAR

set2.acomp:
        Fi         Ga        Gr         Pr        Sh
[1,] 0.05555556 0.5370370 0.16666667 0.1666667 0.07407407
[2,] 0.04347826 0.6739130 0.08695652 0.1521739 0.04347826
[3,] 0.07352941 0.4705882 0.10294118 0.1911765 0.16176471
[4,] 0.04615385 0.5692308 0.07692308 0.2461538 0.06153846
[5,] 0.05479452 0.5205479 0.05479452 0.2465753 0.12328767
[6,] 0.04838710 0.5322581 0.11290323 0.2419355 0.06451613

             Fi          Ga           Gr           Pr           Sh 
(Intercept) 0.002229245 0.0002927936 2.472954e-08 1.361426e-06 0.99747658
x1          0.085750068 0.2770618145 3.810668e-01 2.307283e-01 0.02539301
x2          0.200090962 0.1999211671 2.000300e-01 1.997450e-01 0.20021285
x3          0.090936680 0.1567838336 4.104556e-01 2.970892e-01 0.04473467
x42006      0.200939822 0.2871520918 2.299924e-01 1.429443e-01 0.13897135
x42010             MNAR         MNAR         MNAR         MNAR       MNAR
x42011             MNAR         MNAR         MNAR         MNAR       MNAR
x42012      0.204872911 0.1769349420 8.782860e-02 1.844618e-01 0.34590170
x42013             MNAR         MNAR         MNAR         MNAR       MNAR

set3.acomp:
        Fi         Ga        Gr         Pr        Sh
[1,] 0.05504587 0.5596330 0.07339450 0.2293578 0.082568807
[2,] 0.07339450 0.6146789 0.01834862 0.2293578 0.064220183
[3,] 0.11607143 0.5714286 0.03571429 0.1696429 0.107142857
[4,] 0.10000000 0.4666667 0.15000000 0.1333333 0.150000000
[5,] 0.07777778 0.6111111 0.04444444 0.1888889 0.077777778
[6,] 0.08737623 0.5679455 0.06553218 0.2730507 0.006095338
[7,] 0.10416667 0.5312500 0.06250000 0.2395833 0.062500000
[8,] 0.07228916 0.5542169 0.06024096 0.2650602 0.048192771

             Fi           Ga          Gr         Pr         Sh 
(Intercept) 1.943748e-05 0.058972799 0.89399840 0.04700784 1.524493e-06
x1          4.125158e-02 0.009931625 0.17672213 0.23844959 5.336451e-01
x2          2.000709e-01 0.200086918 0.19954822 0.19948468 2.008093e-01
x3          2.946378e-01 0.146757566 0.07664778 0.13091512 3.510417e-01
x42003      2.347775e-01 0.443477400 0.05214527 0.12408231 1.455175e-01
x42005      2.809541e-01 0.233325976 0.15610948 0.15614758 1.734629e-01
x42006      2.149193e-01 0.031546594 0.07066295 0.03831916 6.445520e-01
x42010              MNAR        MNAR       MNAR       MNAR         MNAR
x42011              MNAR        MNAR       MNAR       MNAR         MNAR
x42012      2.555987e-01 0.170021002 0.18412502 0.16028998 2.299653e-01
x42013              MNAR        MNAR       MNAR       MNAR         MNAR

   I've not found the explanation in my searches and would appreciate
understanding these results.

Rich



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