npbmseSFH: Nonparametric bootstrap mean squared error estimator of the...

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/npbmseSFH.R

Description

Calculates nonparametric bootstrap mean squared error estimates of the spatial EBLUPs obtained by fitting a spatial Fay-Herriot model, in which area effects follow a Simultaneously Autorregressive (SAR) process.

Usage

1
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npbmseSFH(formula, vardir, proxmat, B = 100, method = "REML", MAXITER = 100,
          PRECISION = 0.0001, data)

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 variables in formula.

B

number of bootstrap replicates. Default value is 100.

method

type of fitting method. Currently only "REML" method is available.

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 npbmseSFH is called.

Details

This function uses random number generation. To fix the seed, use set.seed.

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 terms specification of the form first + second indicates all the terms in first together with all the terms in second with any 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:

est

a list with the results of the estimation process: eblup and fit. For the description of these objects, see Value of eblupSFH function.

mse

data frame containing the naive nonparametric bootstrap mean squared error estimates of the spatial EBLUPs (mse) and the bias-corrected nonparametric bootstrap mean squared error estimates of the spatial EBLUPs (msebc).

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.

See Also

eblupSFH, pbmseSFH, mseSFH

Examples

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3
4
5
6
7
8
data(grapes)       # Load data set
data(grapesprox)   # Load proximity matrix

# Obtain the naive and bias-corrected non parametric bootstrap MSE 
# estimates using REML 
set.seed(123)
result <- npbmseSFH(grapehect ~ area + workdays - 1, var, grapesprox, B=2, data=grapes)
result

Example output

Loading required package: MASS
Loading required package: lme4
Loading required package: Matrix

Bootstrap procedure with B = 2 iterations starts.
b = 1 
b = 2 
$est
$est$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

$est$fit
$est$fit$method
[1] "REML"

$est$fit$convergence
[1] TRUE

$est$fit$iterations
[1] 6

$est$fit$estcoef
                 beta   std.error    tvalue      pvalue
Xarea     -0.01236461 0.002071297 -5.969498 2.37984e-09
Xworkdays  0.49978791 0.012429599 40.209495 0.00000e+00

$est$fit$refvar
[1] 69.74899

$est$fit$spatialcorr
[1] 0.6142697

$est$fit$goodness
  loglike       AIC       BIC 
-1210.200  2428.401  2442.853 



$mse
             mse        msebc
1   2.844238e+00 1.807201e+01
2   8.800699e+00 6.069726e+01
3   2.474689e+00 2.754275e+00
4   9.438131e+00 1.812360e+01
5   2.281206e+01 3.506248e+01
6   7.685988e-03 1.627209e-01
7   1.097733e+01 1.282820e+01
8   3.360854e+00 1.591006e+01
9   6.176639e+01 5.877915e+01
10  1.762970e-02 6.658914e-03
11  6.605941e+00 1.167246e+01
12  6.727606e-03 2.231945e-02
13  6.161220e+00 5.955939e+00
14  5.356085e+01 1.506960e+01
15  4.526996e-01 6.452923e+00
16  6.823213e+00 1.410135e+01
17  1.638396e+01 1.024351e+01
18  5.897747e+00 6.508188e+01
19  8.602682e-01 6.635427e+00
20  2.454415e+01 9.389101e+00
21  1.528276e-02 1.370361e-01
22  6.014655e+00 2.355674e+01
23  1.640543e+01 9.055060e+00
24  1.178919e+01 2.522913e+01
25  5.286386e-01 3.506217e+01
26  2.419695e+01 2.024772e+01
27  3.123807e+01 3.068998e+01
28  4.406146e-02 4.092485e-02
29  1.873665e-03 2.813572e-03
30  2.651187e+01 6.390556e+00
31  1.905714e+01 3.862499e+01
32  8.185089e-01 8.896927e+00
33  7.656899e+01 2.250584e+01
34  1.256392e+01 3.155140e+01
35  1.642581e+01 7.299335e+01
36  7.812320e+01 6.272354e+01
37  7.993465e+01 3.925356e+01
38  1.455731e+00 1.484915e+00
39  1.220283e+01 4.296947e+01
40  4.664761e+00 2.144000e+01
41  5.628490e-04 2.620461e-03
42  1.942804e+01 4.182098e+01
43  7.126419e+01 6.146300e+01
44  8.264587e+00 7.413805e+00
45  2.742931e+00 1.063957e+01
46  1.567247e+01 8.337179e+01
47  1.017787e+01 1.967813e+01
48  7.133694e+01 3.951692e+01
49  1.030236e+01 1.625637e+01
50  1.080590e+01 9.032307e+00
51  4.444627e+01 9.336274e+01
52  1.385056e-01 8.611019e-01
53  1.362405e+02 7.520027e+01
54  7.414340e+01 7.246528e+01
55  9.222917e-02 5.967715e-02
56  1.160430e+00 1.779371e+01
57  1.916001e+00 4.687253e+01
58  1.234595e+01 1.707042e+01
59  4.440458e+01 5.926912e+00
60  1.078267e+00 9.689663e-01
61  6.771573e-01 1.232341e+00
62  7.683710e+00 3.316174e+00
63  1.574994e+01 7.422946e+01
64  2.929495e+01 3.999337e+01
65  4.380462e-01 7.034512e+00
66  2.137397e+01 8.461126e+01
67  1.242887e+01 2.713075e+01
68  2.237057e+02 6.246472e+01
69  1.708187e+01 1.841394e+01
70  6.511511e+00 5.437092e+01
71  1.929726e+00 2.156752e+01
72  4.390391e+00 4.909459e+00
73  2.569953e+01 1.090671e+01
74  7.329543e+00 1.315167e+01
75  9.185835e+00 6.682365e+01
76  1.835839e+01 3.988252e+01
77  5.639893e+01 1.056353e+02
78  3.471939e+00 8.313701e-01
79  4.822350e+01 9.149723e+01
80  1.674400e+00 3.985192e+01
81  2.453428e+01 1.521076e+01
82  5.971237e-01 4.635193e+01
83  2.492398e+01 8.832011e+01
84  4.226109e+01 9.925547e+01
85  2.260911e+01 8.959254e+01
86  1.261184e+02 6.607128e+01
87  5.687925e+00 4.589815e+01
88  1.781234e-01 1.199047e+01
89  7.726696e-01 2.857526e-01
90  6.765903e-02 6.460250e-01
91  8.513618e+01 8.679383e+01
92  1.480656e+01 8.656880e+01
93  9.335327e+00 2.516102e+01
94  1.842290e+02 5.618518e+01
95  2.509903e+01 1.066297e+02
96  2.396146e+02 7.366126e+01
97  1.753762e+00 9.326167e+01
98  9.958243e+00 3.340365e+01
99  1.844023e+01 4.370840e+01
100 8.286587e+01 1.008155e+02
101 3.816230e+01 1.135130e+02
102 2.666282e+00 7.264786e+00
103 3.017338e+00 2.785707e+00
104 5.600334e+01 9.527796e+01
105 2.963183e+01 8.209910e+01
106 1.888929e+01 2.349849e+01
107 3.836853e+00 1.389562e+01
108 4.090990e+00 4.943079e+01
109 6.918774e+01 1.037099e+02
110 1.370244e+02 1.089537e+02
111 4.518399e+01 1.122759e+01
112 1.282532e+01 1.063033e+02
113 2.000290e-02 2.528132e-01
114 1.985213e+00 2.473018e+01
115 5.421406e+01 1.228083e+02
116 1.876273e+00 1.112362e+02
117 1.081383e+02 9.268128e+01
118 1.666866e+02 1.177563e+02
119 1.269281e+01 2.146168e+01
120 1.413861e+01 2.664806e+01
121 3.346471e+00 2.187876e+01
122 2.044116e+00 2.775334e+00
123 1.443961e+01 5.291424e+01
124 4.076156e+01 1.136877e+02
125 8.631867e+01 9.364169e+01
126 5.586544e+00 2.258486e+01
127 4.153962e+01 5.954150e+01
128 8.794299e+00 3.490433e+01
129 2.169999e+01 1.202234e+02
130 3.375661e+00 3.495355e+00
131 2.846367e+01 1.201911e+02
132 1.150049e+01 1.134231e+02
133 3.562210e+01 6.691224e+01
134 7.523274e+00 1.191118e+02
135 2.274927e+01 4.428869e+01
136 1.090605e+02 9.385948e+01
137 7.261194e+01 3.785423e+01
138 2.255961e+01 7.244402e+01
139 5.134763e+01 1.088007e+02
140 2.208877e+01 8.862506e+01
141 6.440607e+01 6.255063e+01
142 2.449735e+01 9.199012e+01
143 4.668287e+01 1.099780e+02
144 1.705455e+00 7.712671e+01
145 1.000542e+02 1.033565e+02
146 3.984902e+00 1.023679e+01
147 3.803170e+01 1.014204e+02
148 3.640148e+01 9.873622e+01
149 3.951261e+01 3.986529e+01
150 4.524620e+00 8.094953e+01
151 1.047833e+01 8.200769e+01
152 3.338688e+01 7.728065e+01
153 6.960629e+01 1.046910e+02
154 1.387164e+01 9.293096e+01
155 4.983955e+01 1.067162e+02
156 7.878486e+01 9.332569e+01
157 8.230213e+01 9.500421e+01
158 2.097617e+02 1.197650e+02
159 3.288551e+01 8.037833e+01
160 4.886174e+02 1.138699e+02
161 2.009535e+01 1.010686e+02
162 1.014398e+01 1.001565e+02
163 1.371024e+02 1.101065e+02
164 1.715191e+02 1.245973e+02
165 5.245282e+01 4.203068e+01
166 9.368296e+01 9.660520e+01
167 1.002593e+02 8.245034e+01
168 1.675785e+00 9.491759e+01
169 4.324119e+01 1.037578e+02
170 9.494099e+01 2.795544e+01
171 1.312745e+01 1.170367e+02
172 1.689534e+02 9.665428e+01
173 5.961278e+01 1.357960e+02
174 1.173439e+02 1.157999e+02
175 4.187409e+01 1.067192e+02
176 4.329595e+01 4.655017e+01
177 2.003554e+02 1.178367e+02
178 1.422334e+02 1.108815e+02
179 6.297065e+00 6.366563e+01
180 4.650046e+00 8.560110e+01
181 8.754703e+01 7.230136e+01
182 1.923976e+01 4.683058e+01
183 3.191497e+01 2.185364e+01
184 1.655131e+01 2.378066e+01
185 3.941782e+01 1.946291e+01
186 1.341291e+02 1.084094e+02
187 4.974861e+01 1.242895e+02
188 3.056247e+01 7.969594e+01
189 1.271724e+01 7.351013e+01
190 5.563915e+01 1.186961e+02
191 3.992556e+02 1.031952e+02
192 3.649901e+02 7.167827e+01
193 2.074578e+00 9.704195e+01
194 1.948569e+02 1.027817e+02
195 3.073214e+02 8.240134e+01
196 6.017191e+00 1.122915e+02
197 4.897455e+02 9.113382e+01
198 1.042830e+02 1.054219e+02
199 6.754067e+01 9.177453e+01
200 1.025618e+02 6.387538e+01
201 2.062701e+01 1.017571e+02
202 8.118874e+00 7.400454e+01
203 3.767399e+01 6.667168e+01
204 9.947957e+01 1.022335e+02
205 3.701973e-01 4.040454e+01
206 7.607157e+01 8.289840e+01
207 6.951148e+00 4.681793e+01
208 2.770910e+02 1.036154e+02
209 1.671790e+01 7.031797e+01
210 3.687087e+01 7.088021e+01
211 3.928451e+01 1.002834e+02
212 4.404038e+01 3.192711e+01
213 1.532869e+02 7.728656e+01
214 9.480547e+01 1.035902e+02
215 4.866695e+01 9.731365e+01
216 3.837845e+00 1.379907e+01
217 1.603071e+02 8.401553e+01
218 1.940686e+02 8.204736e+01
219 1.103791e+02 8.705914e+01
220 2.154147e+01 1.128965e+02
221 1.861443e-01 8.983751e-01
222 1.483038e+01 8.058742e+01
223 9.305056e-02 4.252516e+00
224 7.307422e+01 5.452116e+01
225 4.356412e+01 7.183890e+01
226 9.254653e+01 8.959995e+01
227 2.180211e+01 9.063692e+01
228 2.869768e+01 1.159177e+02
229 7.508227e+01 8.694538e+01
230 7.034346e+01 9.222587e+01
231 1.550219e+01 9.547445e+01
232 2.839995e+01 8.919922e+01
233 1.391411e+01 8.215737e+01
234 7.510585e+00 1.130359e+02
235 4.246832e+01 8.721148e+01
236 3.262099e+01 7.663753e+01
237 1.648175e+01 2.918480e+01
238 4.256748e+01 7.157838e+01
239 3.391757e+01 2.122222e+01
240 7.917061e-01 5.843838e+01
241 1.162235e+01 1.102576e+02
242 7.184492e-02 7.480708e+01
243 1.385129e+00 3.787028e+01
244 1.201057e+01 2.922489e+01
245 9.940636e+00 1.758418e+01
246 1.766695e+02 9.176761e+01
247 2.258749e+00 7.648793e+01
248 4.934740e+01 6.717024e+01
249 3.224925e+00 2.692114e+00
250 1.257372e+02 9.470325e+01
251 1.146453e+01 9.513691e+00
252 7.395359e+00 7.974851e+01
253 4.775407e-02 6.220270e-01
254 1.014996e+01 8.152800e+01
255 9.909320e-01 8.827454e+00
256 7.168054e+01 1.173648e+02
257 8.063912e+01 7.053317e+01
258 1.600090e+01 6.282916e+01
259 7.389092e+01 9.130526e+01
260 2.316570e+00 1.211530e+01
261 8.084814e+01 8.183284e+01
262 1.060750e+02 5.314631e+01
263 1.072955e+01 2.970787e+01
264 8.930232e+00 9.376231e+01
265 1.230129e+01 8.180402e+00
266 2.390635e+01 1.077076e+02
267 4.276344e+01 1.140934e+02
268 2.594037e+01 1.049751e+02
269 3.083763e+01 1.104526e+02
270 6.839496e+00 8.983408e+01
271 1.285533e+01 1.151219e+02
272 8.703782e+00 9.308393e+01
273 2.272167e-01 9.342947e+01
274 6.103082e+01 4.897062e+01

sae documentation built on March 26, 2020, 7:52 p.m.