Section 6
I: Weight adjustment for change points
J: Aquahab change points in supplements for 2007 NRI
Andreea Erciulescu
CSSM - NRI Project
April 10, 2012
Andreea Erciulescu (Survey)
April 10, 2012
1 / 16
Part I : Weight adjustment for change points
Previous steps:
• The change point weights have been adjusted
• The weights have been assigned to the no-change points
• The weights for the 1997-level data set are adjusted by broaduse
Andreea Erciulescu (Survey)
April 10, 2012
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Notation
• TC ,gls,t : GLS estimate for coveruse C in year t
• xC ,t,kj = I {point kj is in broaduse C in year t and kj ∈
/ Badj }
P
• X̂C ,t = kj wkj xC ,t,kj
• yC ,t,kj = I {point kj is in broaduse C in year t and kj ∈ Badj }
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April 10, 2012
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Part I : Weight adjustment for change points
New steps:
1. Let Badj be the set of points that are never in a segment coveruse,
never in CRP, never in federal, never in large streams and never in
large water plus the set of points that are never aquahab one1
2. The weights from the previous step are ratio adjusted to give the
correct initial value (usually for the year t − 1 = 1997 ):
Rstart = [
X
wkj yC ,t−1,kj ]−1 [TC ,gls,t−1 − X̂C ,t−1 ].
kj∈Badj
If TC ,gls,t−1 = X̂C ,t−1 , set Rstart = 1.
1
Badj is the set of indexes for points that are never in any of the broaduses 7 - 16, 18,
and never aquahab 1 - details in Section 11C
Andreea Erciulescu (Survey)
April 10, 2012
4 / 16
Part I : Weight adjustment for change points
New steps (cont.):
3. The beginning weights for the adjustment are
Rstart wkj if kj ∈ Badj
wkj∗ =
wkj
otherwise
The wkj∗ will be called wkj at the next step.
Andreea Erciulescu (Survey)
April 10, 2012
5 / 16
More notation
•
yC ,t,kj − yC ,t−1,kj
0
if yC ,t,kj − yC ,t−1,kj > 0
otherwise
yC ,t,kj − yC ,t−1,kj
0
if yC ,t,kj − yC ,t−1,kj < 0
otherwise
zC 1,t,t−1,kj =
•
zC 2,t,t−1,kj =
• zC 3,t,t−1,kj = I {yC ,t,kj − yC ,t−1,kj = 0and yC ,t−1,kj > 0}
P
• ∆Ct,t−1,obs = kj wkj (zC 1,t,t−1,kj + zC 2,t,t−1,kj ) =:
∆C 1,t,t−1,obs + ∆C 2,t,t−1,obs
Andreea Erciulescu (Survey)
April 10, 2012
6 / 16
More notation - cont.
∆Ct,t−1,cont = TC ,gls,t − TC ,gls,t−1 − X̂C ,t + X̂C ,t−1 .
The ∆C 1,t,t−1,obs is the acres that shift into broaduse C between t − 1 and
t that can be adjusted.
The ∆C 2,t,t−1,obs is the acres that shift out of broaduse C between t − 1
and t that can be adjusted.
The ∆C 2,t,t−1,obs is defined with a negative sign.
Andreea Erciulescu (Survey)
April 10, 2012
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Procedure
Step 1. Estimate the acres that stay in C between t and t − 1 from
adjustable points. Let
 ∗
∗
 αt,t−1 if −0.4 ≤ αt,t−1 ≤ 0.4
∗
0.4
if αt,t−1
> 0.4
αt,t−1 =

∗
−0.4 if αt,t−1
< −0.4
∆
−∆
t,t−1,cont
t,t−1,obs
∗
where αt,t−1
= ∆1,t,t−1,obs
−∆2,t,t−1,obs
Note if ∆1,t,t−1,obs − ∆2,t,t−1,obs = 0, then αt,t−1 = 0.
P
Let Ẑ3 = kj wkj z3,t,t−1,kj , so Ẑ3 is the estimate of acres that stay in C
between t and t − 1 estimated from adjustable points.
Andreea Erciulescu (Survey)
April 10, 2012
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Procedure
Step 2. Estimate the acres that move out of C between t and t − 1.
• multiply the weights for points that move out of C between t − 1 and
t by (1 − αt,t−1 ).
• modify the weights on points with z3,t,t−1,kj = 1 to obtain the correct
total for t − 1.
Let the ratio modifier be Rz3 . Then the equation is
Rz3 Ẑ3 − (1 − αt,t−1 )∆2,t,t−1,obs = TC ,gls,t−1 − X̂C ,t−1 .
Therefore, we can define Rz3 as
 ∗
 Rz3
0.5
R̂z3 =

2
below:
∗ ≤ 2.0
if 0.5 ≤ Rz3
∗
if Rz3 < 0.5
∗ > 2.0
if Rz3
where
∗
Rz3
=
[TC ,gls,t−1 + (1 − αt,t−1 )∆2,t,t−1,obs − X̂C ,t−1 ]Ẑ3−1 if Ẑ3 > 0
1
otherwise
Andreea Erciulescu (Survey)
April 10, 2012
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Procedure
Step 2. (cont.) Define the new weights.

(1 + αt,t−1 )wkj if z1,t,t−1,kj =
6 0 and kj ∈ Badj


 (1 − α
)w
if
z
6 0 and kj ∈ Badj
t,t−1
kj
2,t,t−1,kj =
wnew ,kj =

R̂ w
if z3,t,t−1,kj = 1 and kj ∈ Badj

 z3 kj
wkj
otherwise
Notes:
• The adjustment is made for the period 1997 − 2005.
• The weights are ratio adjusted using Rstart before doing the
modification.
• The weights are adjusted sequentially for broaduses in the order
broaduses 5,4,3,2,6,1.
Andreea Erciulescu (Survey)
April 10, 2012
10 / 16
Example - Step 1
• TC ,gls,t = 520, TC ,gls,t−1 = 500, X̂C ,t = 680, X̂C ,t−1 = 450
• ∆C ,t,t−1,cont = 520 − 500 − 680 + 450 = −210
• ∆C 1,t,t−1,obs = 80, ∆C 2,t,t−1,obs = −100,
∆C ,t,t−1,obs = 80 − 100 = −20
∆
−∆
,t,t−1,cont
C ,t,t−1,obs
∗
• Because αt,t−1
= ∆CC1,t,t−1,obs
−∆C 2,t,t−1,obs = −1.056 < −0.4, we have
that αt,t−1 = −0.4.
Andreea Erciulescu (Survey)
April 10, 2012
11 / 16
Example - Step 2
• Ẑ3 =
P
kj
wkj z3,t,t−1,kj = 600.
∗ = [450 − (1 + 0.4) × 100 − 500]/600 = −0.317 < 0.5,
• Because Rz3
we set that R̂z3 = 0.5.
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April 10, 2012
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Example - Step 2: Weights calculation
According to the previous formulas, we can get that:

0.6wkj if z1,t,t−1,kj 6= 0 and kj ∈ Badj



1.4wkj if z2,t,t−1,kj 6= 0 and kj ∈ Badj
wnew ,kj =
0.5wkj if z3,t,t−1,kj = 1 and kj ∈ Badj



wkj
otherwise
Andreea Erciulescu (Survey)
April 10, 2012
13 / 16
Part J: Aquahab Change Points in Supplements for 2007
NRI
Definitions:
1
A new supplement point is a point in the 2004-2006 supplement or in
the 2005-2007 supplement that had not been observed since 1997.
2
A 2001 supplement segment is a 2001 revisited segment, ones all
data are imputed.
Andreea Erciulescu (Survey)
April 10, 2012
14 / 16
Aquahab Change Points in Supplements for 2007 NRI
Procedure:
1 any aquahab change point is converted to a 2001 revisited rotation
point
2 impute all the data that would have been collected in 2001
3 impute all the data elements for 2001 that are entered in 2004 (or
2005) for revisited points
4 impute all segment data and point data for all the points in the
segment, for the entire segment
5 reclassify the segment as a 2001 revisited segment ⇒ no modification
is required in the basic estimation processing
6 the weight for the change point will be assigned in the standard
estimation routine
7 the conditional selection probability for the segment is that for the
category for the 2001 panel and is part of the segment record
8 the weights for the non change points in the segment are also
determined by the estimation program
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April 10, 2012
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End
Thank you!
Andreea Erciulescu (Survey)
April 10, 2012
16 / 16