Data Science and SDGs by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 9789811619199
Publisher: Springer Singapore

S1. no

h6

h5

h4

h3

h2

h1

y

Mean model

1

1

0

1

0

0

0

y1

θ + h4 + h6

2

0

1

0

0

0

1

y2

θ + h1 + h5

3

1

0

0

0

1

1

y3

θ + h1 + h2 + h6

4

0

0

0

1

1

0

y4

θ + h2 + h3

5

0

0

1

1

0

1

y5

θ + h1 + h3 + h4

6

0

1

1

0

1

0

y6

θ + h2 + h4 + h5

7

1

1

0

1

0

0

y7

θ + h3 + h5 + h6

Remark 1: We find remarkable similarity of this model to what is generated in the context of ‘biased spring balance weighing designs’ (Vide Raghavarao 1971 or Shah and Sinha 1989). Naturally, the θ-parameter represents the bias component. The co-efficient matrix X = ((xij)) consists of 0 s and 1 s. It may be noted that in the above, the X- matrix is shown in the reverse order. Multiplication by a permutation matrix P will bring it to the right/standard order. Finally, the linear model (Y, X(*)β, σ2I) is obtained as usual, where X(*) = (1, PX) and β = (θ, h1, h2, …)t.

Remark 2: We recall the implication of the ‘circular model’ in this context. The data-generating sequence is the same as the dummy-sequence on which the circular model is built. Another implication is that the columns h1, h2, … are circular in nature. That is, the columns of matrix X are circular in nature. For a non-circular design/model, the carry-over effects are to be determined separately—depending on the nature of 1 s and 0 s—for each incoming unit/patient.

In case it is believed that there are only K*[<K] h-parameters in the model, the understanding is that the initial set of K*h-parameters viz., h1, h2,…, hK∗ is important and the rest can be ignored from the mean model. For K∗ = 4, the model expectations of successive responses corresponding to the above design would be.

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