eblupSFH: EBLUPs based on a spatial Fay-Herriot model.
In sae: Small Area Estimation
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
This function gives small area estimators based on a spatial Fay-Herriot model, where area effects follow a SAR(1) process. Fitting method can be chosen between REML and ML.
Usage
1
2
Arguments
formula
an object of class formula (or one that can be coerced to that class):
a symbolic description of the model to be fitted. The variables included in formula
must have a length equal to the number of domains D. Details of model specification are given under Details.
vardir
vector containing the D sampling variances of direct estimators for each domain.
The values must be sorted as the variables in formula.
proxmat
D*D proximity matrix or data frame with values in the interval [0,1] containing the proximities between the row and column domains. The rows add up to 1. The rows and columns of this matrix must be sorted as the elements in formula.
method
type of fitting method, to be chosen between "REML" or "ML". Default value is REML.
MAXITER
maximum number of iterations allowed for the Fisher-scoring algorithm. Default value is 100.
PRECISION
convergence tolerance limit for the Fisher-scoring algorithm. Default value is 0.0001.
data
optional data frame containing the variables named in formula and vardir. By default the variables are taken from the environment from which eblupSHF is called.
Details
A typical model has the form response ~ terms where response is the (numeric) response vector and terms is a series of terms which specifies a linear predictor for response. A terms specification of the form first + second indicates all the terms in first together with all the terms in second with duplicates removed.
A formula has an implied intercept term. To remove this use either y ~ x - 1 or y ~ 0 + x. See formula
for more details of allowed formulae.
Value
The function returns a list with the following objects:
eblup
vector with the values of the estimators for the domains.
fit
a list containing the following objects:
method: type of fitting method applied ("REML" or "ML").
convergence: a logical value equal to TRUE if Fisher-scoring algorithm converges in less than MAXITER iterations.
iterations: number of iterations performed by the Fisher-scoring algorithm.
estcoef: a data frame with the estimated model coefficients in the first column (beta),
their asymptotic standard errors in the second column (std.error),
the t statistics in the third column (tvalue) and the p-values of the significance
of each coefficient in last column (pvalue).
refvar: estimated random effects variance.
spatialcorr: estimated spatial correlation parameter.
goodness: vector containing three goodness-of-fit measures: loglikehood, AIC and BIC.
In case that formula, vardir or proxmat contain NA values a message is printed and no action is done.
Author(s)
Isabel Molina, Monica Pratesi and Nicola Salvati.
References
- Small Area Methods for Poverty and Living Conditions Estimates (SAMPLE), funded by European Commission, Collaborative Project 217565, Call identifier FP7-SSH-2007-1.
- Molina, I., Salvati, N. and Pratesi, M. (2009). Bootstrap for estimating the MSE of the Spatial EBLUP. Computational Statistics 24, 441-458.
- Petrucci, A. and Salvati, N. (2006). Small area estimation for spatial correlation in watershed erosion assessment.
Journal of Agricultural, Biological and Environmental Statistics 11, 169-182.
- Pratesi, M. and Salvati, N. (2008). Small area estimation: the EBLUP estimator based on spatially correlated random area effects.
Statistical Methods & Applications 17, 113-141.
See Also
Examples
1
2
3
4
5
6
7
8
9
10
11
12
data(grapes) # Load data set
data(grapesprox) # Load proximity matrix
# Fit Spatial Fay-Herriot model using ML method
resultML <- eblupSFH(grapehect ~ area + workdays - 1, var, grapesprox,
method="ML", data=grapes)
resultML
# Fit Spatial Fay-Herriot model using REML method
resultREML <- eblupSFH(grapehect ~ area + workdays - 1, var, grapesprox,
data=grapes)
resultREML
Example output
Loading required package: nlme
Loading required package: MASS
$eblup
[,1]
1 31.2571366
2 71.6565845
3 73.8829196
4 62.2841484
5 39.5308835
6 78.5373862
7 50.1055964
8 41.2263981
9 109.4093594
10 10.2332430
11 80.0567852
12 78.4564565
13 60.5216891
14 52.7110630
15 59.4059338
16 69.0733769
17 103.0358109
18 43.0376736
19 34.9705054
20 73.0570173
21 71.6305528
22 84.2942451
23 59.9985107
24 66.6550468
25 70.8457003
26 58.7060896
27 75.1584138
28 15.8076017
29 2.0184207
30 130.1651225
31 36.2506135
32 22.4582624
33 15.5453618
34 63.7437409
35 60.9416655
36 90.2747710
37 54.2737572
38 41.7060418
39 83.1891749
40 58.7945444
41 0.6296585
42 98.3365518
43 76.5639619
44 38.9012443
45 17.1897564
46 138.7458221
47 48.4408672
48 52.3650391
49 28.7725830
50 77.6912187
51 64.2381503
52 38.0107638
53 58.9726064
54 39.9604880
55 19.6400166
56 95.0019455
57 74.4529403
58 58.8731120
59 57.5307451
60 41.5563091
61 96.3267492
62 66.6626507
63 81.7564908
64 52.9329892
65 38.4135642
66 63.8083122
67 46.3935315
68 43.6491451
69 44.5430817
70 50.2326839
71 78.5652106
72 62.5336326
73 35.7404025
74 73.8278276
75 52.7127620
76 86.1671992
77 103.1685856
78 52.5739141
79 46.7438946
80 34.6463614
81 144.5388615
82 78.2806430
83 90.1509841
84 73.9552097
85 52.8541209
86 50.1336880
87 24.3813547
88 57.6624491
89 36.2442600
90 26.7916040
91 30.8260040
92 40.4945601
93 161.7345625
94 32.2696092
95 49.2624511
96 97.0983242
97 46.8936262
98 47.6331473
99 68.5548702
100 72.5679566
101 72.9207955
102 50.4262908
103 106.6644627
104 61.3234348
105 37.0177214
106 54.7530544
107 30.3319063
108 47.6724771
109 49.5637769
110 85.3348212
111 29.6114648
112 99.5816154
113 94.8991783
114 76.2080012
115 81.9817368
116 66.1058067
117 66.9672190
118 61.9454969
119 51.6259968
120 66.8841082
121 39.4323778
122 36.0874984
123 72.5341149
124 61.9806544
125 53.0519669
126 44.4142545
127 27.8057962
128 64.0726720
129 116.1241404
130 56.8226201
131 118.7969663
132 58.2583539
133 62.6770553
134 128.3176632
135 39.0196390
136 47.7733704
137 56.5838926
138 52.6086162
139 63.4773596
140 54.5707260
141 153.8960106
142 67.2853271
143 71.6824719
144 47.9948304
145 70.4068895
146 19.6685819
147 73.9936258
148 36.6553805
149 82.1917874
150 25.3320132
151 57.0787989
152 73.8823648
153 71.9995960
154 79.1102127
155 39.8691805
156 72.9722124
157 34.8268215
158 112.1174723
159 45.2070954
160 79.6465607
161 59.8649513
162 68.0170117
163 89.4288024
164 143.5199710
165 140.9778530
166 59.6112614
167 31.3498354
168 57.8377606
169 74.8642556
170 108.6159477
171 78.0477770
172 71.8696746
173 216.1489762
174 121.4248739
175 19.8307445
176 51.5444224
177 64.3876663
178 35.0488766
179 34.2581905
180 52.1698091
181 55.1143751
182 51.3932915
183 88.8923297
184 60.5062181
185 72.0946965
186 67.9996235
187 167.5943931
188 79.3921557
189 88.6387694
190 106.9205213
191 84.8028113
192 23.7670753
193 28.6373826
194 48.9580029
195 68.4149461
196 68.6009218
197 17.9453849
198 55.5774211
199 84.2433532
200 102.8574841
201 37.6714008
202 27.7713359
203 53.1466704
204 88.9922422
205 55.6620157
206 26.3971742
207 51.0118947
208 46.2535603
209 96.9251567
210 58.9645809
211 75.1200604
212 52.2421521
213 70.3246376
214 120.1460918
215 53.9083444
216 30.2498960
217 38.1943007
218 54.3492624
219 95.3340076
220 100.4679579
221 49.6672258
222 53.7532926
223 39.9058070
224 96.2785835
225 75.2770396
226 118.1056690
227 57.7993445
228 220.6941375
229 82.2203411
230 90.8117563
231 91.4824044
232 61.0794578
233 49.0188931
234 69.0659050
235 44.9272478
236 109.9512289
237 55.7020686
238 52.3964181
239 85.6598396
240 75.7578853
241 50.2374927
242 57.0745136
243 35.5549663
244 29.0189521
245 33.0785540
246 54.1355475
247 32.1155910
248 63.8175726
249 16.1157392
250 44.0914980
251 40.8441234
252 87.6735913
253 46.4325558
254 62.8084239
255 114.3535108
256 167.9654691
257 59.1685443
258 106.9977092
259 91.4451279
260 43.8867981
261 93.1682370
262 65.8409008
263 81.3622034
264 43.9925968
265 53.5930920
266 158.4691688
267 121.0510081
268 123.6444498
269 111.4957129
270 46.4983395
271 54.2962505
272 88.4482394
273 89.0357233
274 24.2158794
$fit
$fit$method
[1] "ML"
$fit$convergence
[1] TRUE
$fit$iterations
[1] 6
$fit$estcoef
beta std.error tvalue pvalue
area -0.01232217 0.002055485 -5.994777 2.037649e-09
workdays 0.49943463 0.012297241 40.613553 0.000000e+00
$fit$refvar
[1] 69.22195
$fit$spatialcorr
[1] 0.6045822
$fit$goodness
loglike AIC BIC
-1210.188 2428.377 2442.830
$eblup
[,1]
1 31.2473574
2 71.7091179
3 73.8818783
4 62.3119391
5 39.5331862
6 78.5372343
7 50.1179508
8 41.2215285
9 109.4147029
10 10.2332370
11 80.0601239
12 78.4564549
13 60.5230608
14 52.7016378
15 59.4096364
16 69.0928112
17 103.0588057
18 43.0519058
19 34.9766345
20 73.0541907
21 71.6304269
22 84.3444241
23 59.9903091
24 66.7118986
25 70.9238814
26 58.7022975
27 75.1170882
28 15.8075814
29 2.0184115
30 130.1856472
31 36.2229314
32 22.4439174
33 15.5070131
34 63.6980686
35 60.9591184
36 90.2772340
37 54.2759008
38 41.7050918
39 83.2384378
40 58.7763103
41 0.6296496
42 98.3732451
43 76.5099460
44 38.8980894
45 17.1595737
46 138.7936677
47 48.4546593
48 52.3064698
49 28.7510665
50 77.6802874
51 64.1364943
52 38.0073916
53 58.9717040
54 39.8908532
55 19.6398611
56 94.9963280
57 74.4423215
58 58.8579486
59 57.5260939
60 41.5551500
61 96.3268999
62 66.6611015
63 81.7867520
64 52.9305981
65 38.4023021
66 63.8288160
67 46.3570692
68 43.6399537
69 44.5249631
70 50.1819752
71 78.5692175
72 62.5305710
73 35.7362787
74 73.8062057
75 52.5933467
76 86.1573787
77 103.2219022
78 52.5712512
79 46.6804467
80 34.5747116
81 144.5602785
82 78.3065162
83 90.2131325
84 73.8694984
85 52.7152760
86 50.0417446
87 24.2862729
88 57.6560481
89 36.2432837
90 26.7900529
91 30.7297622
92 40.4096826
93 161.7055453
94 32.1926932
95 49.1407259
96 97.1633974
97 46.7796556
98 47.6425546
99 68.4741555
100 72.5824824
101 72.8469544
102 50.4263793
103 106.6669401
104 61.2470009
105 36.8935562
106 54.7449782
107 30.3188084
108 47.6734216
109 49.4521361
110 85.4316873
111 29.6023981
112 99.6132590
113 94.8995528
114 76.2335943
115 81.9153663
116 66.2122503
117 67.1170202
118 61.8854625
119 51.6299238
120 66.8980289
121 39.4326384
122 36.0839576
123 72.5438949
124 61.9240457
125 53.0018941
126 44.4072469
127 27.7115606
128 64.0778863
129 116.1888414
130 56.8317880
131 118.8112966
132 58.3909477
133 62.7837687
134 128.4414941
135 38.9784976
136 47.8681853
137 56.5552263
138 52.6330415
139 63.6887630
140 54.5192809
141 153.9813108
142 67.3042478
143 71.6443692
144 48.0480754
145 70.5613875
146 19.6409531
147 74.0130735
148 36.6854652
149 82.2199326
150 25.2402524
151 57.1759865
152 73.9204808
153 71.9698205
154 79.2150558
155 39.7829481
156 73.0716676
157 34.8621573
158 112.1769920
159 45.2198814
160 79.6475715
161 59.9084573
162 67.8699683
163 89.4026635
164 143.5744398
165 141.0363210
166 59.6556119
167 31.2103381
168 57.9933141
169 74.8360370
170 108.6727570
171 78.1318329
172 72.0583145
173 216.2827762
174 121.4483874
175 19.6583014
176 51.5111084
177 64.4297571
178 34.9282768
179 34.1413486
180 52.2789295
181 55.2791448
182 51.3956234
183 88.9436840
184 60.5301515
185 72.0956385
186 68.0334461
187 167.7150411
188 79.5236227
189 88.7663169
190 107.0139596
191 84.8582289
192 23.6324440
193 28.5023365
194 48.9339783
195 68.4684320
196 68.6961935
197 17.7674981
198 55.6132378
199 84.3077505
200 102.9240691
201 37.7408894
202 27.6968677
203 53.1509077
204 89.0877447
205 55.6892779
206 26.2918268
207 51.0226949
208 46.3019214
209 96.9827547
210 58.9711892
211 75.1042635
212 52.2981673
213 70.4331390
214 120.2950007
215 53.9998798
216 30.2496818
217 38.1692378
218 54.4569331
219 95.2668932
220 100.5901469
221 49.6676537
222 53.7248883
223 39.9167562
224 96.3776627
225 75.3164597
226 118.1879058
227 57.7844432
228 220.6942183
229 82.2507653
230 90.9046856
231 91.5620846
232 61.0939697
233 49.0669026
234 69.1646421
235 45.0162202
236 110.0200061
237 55.7036153
238 52.4814887
239 85.6748799
240 75.7926795
241 50.3440447
242 57.0144100
243 35.5475187
244 28.9814123
245 33.0722825
246 54.0833885
247 32.0369082
248 63.8488595
249 16.1143170
250 44.1173087
251 40.8426739
252 87.6827647
253 46.4316880
254 62.7415613
255 114.3592705
256 168.1576484
257 59.1927970
258 107.1126999
259 91.5921246
260 43.8730244
261 93.2190909
262 65.9403041
263 81.4435792
264 43.9471543
265 53.5850714
266 158.6539096
267 121.2368263
268 123.8153749
269 111.5639690
270 46.4971916
271 54.2536820
272 88.5520554
273 89.0878716
274 24.2952980
$fit
$fit$method
[1] "REML"
$fit$convergence
[1] TRUE
$fit$iterations
[1] 6
$fit$estcoef
beta std.error tvalue pvalue
area -0.01236461 0.002071297 -5.969498 2.37984e-09
workdays 0.49978791 0.012429599 40.209495 0.00000e+00
$fit$refvar
[1] 69.74899
$fit$spatialcorr
[1] 0.6142697
$fit$goodness
loglike AIC BIC
-1210.200 2428.401 2442.853
sae documentation built on March 26, 2020, 7:52 p.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
This function gives small area estimators based on a spatial Fay-Herriot model, where area effects follow a SAR(1) process. Fitting method can be chosen between REML and ML.
Usage
1 2 |
Arguments
formula |
an object of class |
vardir |
vector containing the |
proxmat |
|
method |
type of fitting method, to be chosen between |
MAXITER |
maximum number of iterations allowed for the Fisher-scoring algorithm. Default value is |
PRECISION |
convergence tolerance limit for the Fisher-scoring algorithm. Default value is |
data |
optional data frame containing the variables named in |
Details
A typical model has the form response ~ terms where response is the (numeric) response vector and terms is a series of terms which specifies a linear predictor for response. A terms specification of the form first + second indicates all the terms in first together with all the terms in second with duplicates removed.
A formula has an implied intercept term. To remove this use either y ~ x - 1 or y ~ 0 + x. See formula
for more details of allowed formulae.
Value
The function returns a list with the following objects:
eblup |
vector with the values of the estimators for the domains. |
fit |
a list containing the following objects:
|
In case that formula, vardir or proxmat contain NA values a message is printed and no action is done.
Author(s)
Isabel Molina, Monica Pratesi and Nicola Salvati.
References
- Small Area Methods for Poverty and Living Conditions Estimates (SAMPLE), funded by European Commission, Collaborative Project 217565, Call identifier FP7-SSH-2007-1.
- Molina, I., Salvati, N. and Pratesi, M. (2009). Bootstrap for estimating the MSE of the Spatial EBLUP. Computational Statistics 24, 441-458.
- Petrucci, A. and Salvati, N. (2006). Small area estimation for spatial correlation in watershed erosion assessment. Journal of Agricultural, Biological and Environmental Statistics 11, 169-182.
- Pratesi, M. and Salvati, N. (2008). Small area estimation: the EBLUP estimator based on spatially correlated random area effects. Statistical Methods & Applications 17, 113-141.
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 | data(grapes) # Load data set
data(grapesprox) # Load proximity matrix
# Fit Spatial Fay-Herriot model using ML method
resultML <- eblupSFH(grapehect ~ area + workdays - 1, var, grapesprox,
method="ML", data=grapes)
resultML
# Fit Spatial Fay-Herriot model using REML method
resultREML <- eblupSFH(grapehect ~ area + workdays - 1, var, grapesprox,
data=grapes)
resultREML
|
Example output
Loading required package: nlme
Loading required package: MASS
$eblup
[,1]
1 31.2571366
2 71.6565845
3 73.8829196
4 62.2841484
5 39.5308835
6 78.5373862
7 50.1055964
8 41.2263981
9 109.4093594
10 10.2332430
11 80.0567852
12 78.4564565
13 60.5216891
14 52.7110630
15 59.4059338
16 69.0733769
17 103.0358109
18 43.0376736
19 34.9705054
20 73.0570173
21 71.6305528
22 84.2942451
23 59.9985107
24 66.6550468
25 70.8457003
26 58.7060896
27 75.1584138
28 15.8076017
29 2.0184207
30 130.1651225
31 36.2506135
32 22.4582624
33 15.5453618
34 63.7437409
35 60.9416655
36 90.2747710
37 54.2737572
38 41.7060418
39 83.1891749
40 58.7945444
41 0.6296585
42 98.3365518
43 76.5639619
44 38.9012443
45 17.1897564
46 138.7458221
47 48.4408672
48 52.3650391
49 28.7725830
50 77.6912187
51 64.2381503
52 38.0107638
53 58.9726064
54 39.9604880
55 19.6400166
56 95.0019455
57 74.4529403
58 58.8731120
59 57.5307451
60 41.5563091
61 96.3267492
62 66.6626507
63 81.7564908
64 52.9329892
65 38.4135642
66 63.8083122
67 46.3935315
68 43.6491451
69 44.5430817
70 50.2326839
71 78.5652106
72 62.5336326
73 35.7404025
74 73.8278276
75 52.7127620
76 86.1671992
77 103.1685856
78 52.5739141
79 46.7438946
80 34.6463614
81 144.5388615
82 78.2806430
83 90.1509841
84 73.9552097
85 52.8541209
86 50.1336880
87 24.3813547
88 57.6624491
89 36.2442600
90 26.7916040
91 30.8260040
92 40.4945601
93 161.7345625
94 32.2696092
95 49.2624511
96 97.0983242
97 46.8936262
98 47.6331473
99 68.5548702
100 72.5679566
101 72.9207955
102 50.4262908
103 106.6644627
104 61.3234348
105 37.0177214
106 54.7530544
107 30.3319063
108 47.6724771
109 49.5637769
110 85.3348212
111 29.6114648
112 99.5816154
113 94.8991783
114 76.2080012
115 81.9817368
116 66.1058067
117 66.9672190
118 61.9454969
119 51.6259968
120 66.8841082
121 39.4323778
122 36.0874984
123 72.5341149
124 61.9806544
125 53.0519669
126 44.4142545
127 27.8057962
128 64.0726720
129 116.1241404
130 56.8226201
131 118.7969663
132 58.2583539
133 62.6770553
134 128.3176632
135 39.0196390
136 47.7733704
137 56.5838926
138 52.6086162
139 63.4773596
140 54.5707260
141 153.8960106
142 67.2853271
143 71.6824719
144 47.9948304
145 70.4068895
146 19.6685819
147 73.9936258
148 36.6553805
149 82.1917874
150 25.3320132
151 57.0787989
152 73.8823648
153 71.9995960
154 79.1102127
155 39.8691805
156 72.9722124
157 34.8268215
158 112.1174723
159 45.2070954
160 79.6465607
161 59.8649513
162 68.0170117
163 89.4288024
164 143.5199710
165 140.9778530
166 59.6112614
167 31.3498354
168 57.8377606
169 74.8642556
170 108.6159477
171 78.0477770
172 71.8696746
173 216.1489762
174 121.4248739
175 19.8307445
176 51.5444224
177 64.3876663
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269 111.4957129
270 46.4983395
271 54.2962505
272 88.4482394
273 89.0357233
274 24.2158794
$fit
$fit$method
[1] "ML"
$fit$convergence
[1] TRUE
$fit$iterations
[1] 6
$fit$estcoef
beta std.error tvalue pvalue
area -0.01232217 0.002055485 -5.994777 2.037649e-09
workdays 0.49943463 0.012297241 40.613553 0.000000e+00
$fit$refvar
[1] 69.22195
$fit$spatialcorr
[1] 0.6045822
$fit$goodness
loglike AIC BIC
-1210.188 2428.377 2442.830
$eblup
[,1]
1 31.2473574
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270 46.4971916
271 54.2536820
272 88.5520554
273 89.0878716
274 24.2952980
$fit
$fit$method
[1] "REML"
$fit$convergence
[1] TRUE
$fit$iterations
[1] 6
$fit$estcoef
beta std.error tvalue pvalue
area -0.01236461 0.002071297 -5.969498 2.37984e-09
workdays 0.49978791 0.012429599 40.209495 0.00000e+00
$fit$refvar
[1] 69.74899
$fit$spatialcorr
[1] 0.6142697
$fit$goodness
loglike AIC BIC
-1210.200 2428.401 2442.853
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