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I am performing an experiment to identify significance in certain factors and covarites. I am using an ANCOVA model with 6 regression covariates, 1 treatment factor and a blocking factor and am including interactions between the covariates and the treatment factor. Are my sums of squares(via aov function) still valid if I get unestimable coefficients in R? I am not interested in making inference on the coefficients, so I was thinking whether non-estimable coefficients can just be ignored.

EDIT for example to MDEWEY comment.

data.frame(x1,x2,x3,x4,x5,x6)
    x1 x2 x3 x4 x5 x6
1   12  0  0  0  0  0
2   12  0  0  0  0  0
3   12  0  0  0  0  0
4   12  0  0  0  0  0
5    0 12  0  0  0  0
6    0 12  0  0  0  0
7    0 12  0  0  0  0
8    0 12  0  0  0  0
9    0  0 12  0  0  0
10   0  0 12  0  0  0
11   0  0 12  0  0  0
12   0  0 12  0  0  0
13   0  0  0 12  0  0
14   0  0  0 12  0  0
15   0  0  0 12  0  0
16   0  0  0 12  0  0
17   0  0  0  0 12  0
18   0  0  0  0 12  0
19   0  0  0  0 12  0
20   0  0  0  0 12  0
21   0  0  0  0  0 12
22   0  0  0  0  0 12
23   0  0  0  0  0 12
24   0  0  0  0  0 12
25   6  6  0  0  0  0
26   6  6  0  0  0  0
27   6  6  0  0  0  0
28   6  6  0  0  0  0
29   6  0  6  0  0  0
30   6  0  6  0  0  0
31   6  0  6  0  0  0
32   6  0  6  0  0  0
33   6  0  0  6  0  0
34   6  0  0  6  0  0
35   6  0  0  6  0  0
36   6  0  0  6  0  0
37   6  0  0  0  6  0
38   6  0  0  0  6  0
39   6  0  0  0  6  0
40   6  0  0  0  6  0
41   6  0  0  0  0  6
42   6  0  0  0  0  6
43   6  0  0  0  0  6
44   6  0  0  0  0  6
45   0  6  6  0  0  0
46   0  6  6  0  0  0
47   0  6  6  0  0  0
48   0  6  6  0  0  0
49   0  6  0  6  0  0
50   0  6  0  6  0  0
51   0  6  0  6  0  0
52   0  6  0  6  0  0
53   0  6  0  0  6  0
54   0  6  0  0  6  0
55   0  6  0  0  6  0
56   0  6  0  0  6  0
57   0  6  0  0  0  6
58   0  6  0  0  0  6
59   0  6  0  0  0  6
60   0  6  0  0  0  6
61   0  0  6  6  0  0
62   0  0  6  6  0  0
63   0  0  6  6  0  0
64   0  0  6  6  0  0
65   0  0  6  0  6  0
66   0  0  6  0  6  0
67   0  0  6  0  6  0
68   0  0  6  0  6  0
69   0  0  6  0  0  6
70   0  0  6  0  0  6
71   0  0  6  0  0  6
72   0  0  6  0  0  6
73   0  0  0  6  6  0
74   0  0  0  6  6  0
75   0  0  0  6  6  0
76   0  0  0  6  6  0
77   0  0  0  6  0  6
78   0  0  0  6  0  6
79   0  0  0  6  0  6
80   0  0  0  6  0  6
81   0  0  0  0  6  6
82   0  0  0  0  6  6
83   0  0  0  0  6  6
84   0  0  0  0  6  6
85   4  4  4  0  0  0
86   4  4  4  0  0  0
87   4  4  4  0  0  0
88   4  4  4  0  0  0
89   4  4  0  4  0  0
90   4  4  0  4  0  0
91   4  4  0  4  0  0
92   4  4  0  4  0  0
93   4  4  0  0  4  0
94   4  4  0  0  4  0
95   4  4  0  0  4  0
96   4  4  0  0  4  0
97   4  4  0  0  0  4
98   4  4  0  0  0  4
99   4  4  0  0  0  4
100  4  4  0  0  0  4
101  4  0  4  4  0  0
102  4  0  4  4  0  0
103  4  0  4  4  0  0
104  4  0  4  4  0  0
105  4  0  4  0  4  0
106  4  0  4  0  4  0
107  4  0  4  0  4  0
108  4  0  4  0  4  0
109  4  0  4  0  0  4
110  4  0  4  0  0  4
111  4  0  4  0  0  4
112  4  0  4  0  0  4
113  4  0  0  4  4  0
114  4  0  0  4  4  0
115  4  0  0  4  4  0
116  4  0  0  4  4  0
117  4  0  0  4  0  4
118  4  0  0  4  0  4
119  4  0  0  4  0  4
120  4  0  0  4  0  4
121  4  0  0  0  4  4
122  4  0  0  0  4  4
123  4  0  0  0  4  4
124  4  0  0  0  4  4
125  0  4  4  4  0  0
126  0  4  4  4  0  0
127  0  4  4  4  0  0
128  0  4  4  4  0  0
129  0  4  4  0  4  0
130  0  4  4  0  4  0
131  0  4  4  0  4  0
132  0  4  4  0  4  0
133  0  4  4  0  0  4
134  0  4  4  0  0  4
135  0  4  4  0  0  4
136  0  4  4  0  0  4
137  0  4  0  4  4  0
138  0  4  0  4  4  0
139  0  4  0  4  4  0
140  0  4  0  4  4  0
141  0  4  0  4  0  4
142  0  4  0  4  0  4
143  0  4  0  4  0  4
144  0  4  0  4  0  4
145  0  4  0  0  4  4
146  0  4  0  0  4  4
147  0  4  0  0  4  4
148  0  4  0  0  4  4
149  0  0  4  4  4  0
150  0  0  4  4  4  0
151  0  0  4  4  4  0
152  0  0  4  4  4  0
153  0  0  4  4  0  4
154  0  0  4  4  0  4
155  0  0  4  4  0  4
156  0  0  4  4  0  4
157  0  0  4  0  4  4
158  0  0  4  0  4  4
159  0  0  4  0  4  4
160  0  0  4  0  4  4
161  0  0  0  4  4  4
162  0  0  0  4  4  4
163  0  0  0  4  4  4
164  0  0  0  4  4  4
Improve this question
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3
  • $\begingroup$ Would it not be wise to find out why your model cannot be estimated first? $\endgroup$
    – mdewey
    Aug 21, 2016 at 10:46
  • $\begingroup$ @mdewey I know it is because of the regression covariates. When I add the last regression covariate, the alias() shows me that x6 is a linear combination of the intercept and x1,x2,x3,x4,x5. This linear dependence is quite obvious by the design. x1,x2,x3,x4,x5,x6 contain only 4 values each (0,4,6,12) and they are in a pattern as updated. $\endgroup$
    – tintinthong
    Aug 21, 2016 at 17:22
  • $\begingroup$ But why would it matter, if I am not interested in what the coefficients of the linear model mean(added inside question). I am more interested in considering x1,x2,x3,x4,x5,x6 together as an individual vector space on its own. $\endgroup$
    – tintinthong
    Aug 21, 2016 at 17:28

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