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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