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Introduction
Traditional linear models, such as the output of the R function
lm(), are often loaded with a set of strong assumptions.
Take univariate regression:
\[ Y = q+mX+\varepsilon. (\#eq:lm) \] This equation assumes that:
- The conditional mean \(\mathbb E(Y\vert X) = q + mX\), a linear function of \(X\).
- The conditional variance \(\mathbb {V}(Y \vert X)=\mathbb{V}(\varepsilon\vert X)\) is independent of \(X\).
- The conditional distribution \(Y\vert X\) is gaussian.
- In a set of measurements \(\left\{\left(X_i,Y_i\right)\right\}_{i = 1,\, \dots, \,N}\), \(Y_i\) and the set \(\left\{ X_j, Y_j\right\} _{j\neq i}\) are conditionally independent of each other, given the value of the corresponding regressor \(X_i\).1
The last assumption is satisfied in many practical situations, and we will take it here for granted2. What happens when the first three assumptions are violated (that is “frequently” to “almost always”, depending on context)?
A comprehensive discussion is provided by (Buja et al. 2019). These authors show that:
If the conditional mean \(\mathbb E (Y \vert X)\) is not linear (“first order misspecification”), then the Ordinary Least Squares (OLS) regression coefficients \(\hat \beta\) consistently estimate: \[ \beta \equiv \text{arg } \min _{\beta^\prime} \mathbb E((Y-X\beta^\prime)^2) (\#eq:target) \] which can be thought as the “best linear approximation of the response”3.
Both non-linearity in the sense of the previous point, and \(X\)-dependence in \(\mathbb{V}(Y \vert X)\) (“second order misspecification”) affect the sampling distribution of \(\hat \beta\) and, in particular, \(\mathbb{V}(\hat \beta)\), which is the relevant quantity for inference in the large-sample limit.
Both problems can be efficiently addressed through the so-called “sandwich” estimators for the covariance matrix of \(\hat \beta\) (White 1980), whose consistency is robust to both type of misspecification.
Details can be found in the mentioned reference. The rest of the post
illustrates with examples how to compute “sandwich” estimates in
R, and why you may want to do so.
Fitting misspecified linear models in R
The {sandwich}
package (available on CRAN) provides estimators for the regression
coefficients’ variance-covariance matrix \(\mathbb V (\hat \beta)\) that are robust to
first and second order misspecification. These can be readily used with
lm objects, as in the example below:
fit <- lm(mpg ~ wt, data = mtcars)
stats::vcov(fit) # standard vcov (linear model trusting estimate)
(Intercept) wt
(Intercept) 3.525484 -1.005693
wt -1.005693 0.312594
sandwich::vcovHC(fit) # sandwich vcov (model-robust estimate)
(Intercept) wt
(Intercept) 5.889249 -1.7418581
wt -1.741858 0.5448011
It is important to note that both functions
stats::vcov() and sandwich::vcovHC() employ
the same point estimates of regression coefficients
to compute \(\mathbb V (\hat
\beta)\):
fit
Call:
lm(formula = mpg ~ wt, data = mtcars)
Coefficients:
(Intercept) wt
37.285 -5.344
The difference between these functions lies in the different assumptions they make on the linear model residuals, which leads to different estimates for \(\mathbb{V}(\hat \beta)\).
Effects of misspecification
This section illustrates some consequences of model misspecification through simulation. The examples use:
library(dplyr) library(ggplot2)
For convenience, we define some helpers to be used in the following examples. The function below returns random generators for the generic additive error model \(Y = f(X) + \varepsilon\), where the distribution of the noise term \(\varepsilon\) may in general depend on \(X\). Both \(X\) and \(Y\) are assumed here and below to be 1-dimensional.
rxy_fun <- function(rx, f, reps) {
res <- function(n) {
x <- rx(n) # X has marginal distribution 'rx'
y <- f(x) + reps(x) # Y has conditional mean 'f(x)' and noise 'reps(x)'
return(tibble(x = x, y = y))
}
return(structure(res, class = "rxy"))
}
plot.rxy <- function(x, N = 1000, seed = 840) {
set.seed(seed)
ggplot(data = x(N), aes(x = x, y = y)) +
geom_point(alpha = 0.3) +
geom_smooth(method = "lm", se = FALSE)
}
The following function simulates fitting the linear model
y ~ x over multiple datasets generated according to a
function rxy().
lmsim <- function(rxy, N = 100, vcov = stats::vcov, B = 1e3, seed = 840)
{
set.seed(seed)
res <- list(coef = matrix(nrow = B, ncol = 2), vcov = vector("list", B))
colnames(res$coef) <- c("(Intercept)", "x")
class(res) <- "lmsim"
for (b in 1:B) {
.fit <- lm(y ~ ., data = rxy(N))
res$coef[b, ] <- coef(.fit) # Store intercept and slope in B x 2 matrix
res$vcov[[b]] <- vcov(.fit) # Store vcov estimates in length B list.
}
return(res)
}
print.lmsim <- function(x)
{
cat("Simulation results:\n\n")
cat("* Model-trusting vcov (average of vcov estimates):\n")
print( avg_est_vcov <- Reduce("+", x$vcov) / length(x$vcov) )
cat("\n* Simulation-based vcov (vcov of coefficient estimates):\n")
print( emp_vcov <- cov(x$coef))
cat("\n* Ratio (1st / 2nd):\n")
print( avg_est_vcov / emp_vcov )
return(invisible(x))
}
The print method defined above shows a comparison of the covariance matrices obtained by:
- Averaging variance-covariance estimates from the various simulations, and
- Taking the variance-covariance matrix of regression coefficients obtained in the simulations.
The first one can be considered a “model-trusting” estimate (where
the actual “model” is specified by the vcov argument of
lmsim(), i.e. stats::vcov and
sandwich::vcovHC for the traditional and sandwich
estimates, respectively). The second one is a model-free
simulation-based estimate of the true \(\mathbb{V}(\hat \beta)\). The comparison
between the two4 provides a measure of the asymptotic bias
of the model-trusting estimate.
Example 1: First order misspecification
\[ Y = X ^ 2 + \varepsilon,\quad X \sim \text{Unif} (0,1),\qquad \varepsilon \sim \mathcal N (0,0.01) \]
rxy_01 <- rxy_fun(
rx = runif,
f = \(x) x^2,
reps = \(x) rnorm(length(x), sd = .01)
)
In this model, \(\mathbb E (Y \vert X)\) is not linear in \(X\) (first order misspecification), but the remaining assumptions of the linear model hold. This is how a typical linear fit of data generated from this model looks like:
plot(rxy_01, N = 300)
Here the effect of misspecification on the variance-covariance model trusting estimates is to underestimate true covariance values (by a factor as large as 40%!):
lmsim(rxy_01)
$coef
(Intercept) x
[1,] -0.1492042 0.9848331
[2,] -0.1672965 0.9938356
[3,] -0.1741689 1.0133387
[4,] -0.1343376 0.9338718
[5,] -0.1522985 0.9771531
[6,] -0.1617622 0.9735575
[7,] -0.1850168 1.0479047
[8,] -0.1725564 1.0150846
[9,] -0.1519079 0.9797259
[10,] -0.1701713 1.0003935
[11,] -0.1776876 1.0118800
[12,] -0.1726425 0.9886916
[13,] -0.1530396 0.9900055
[14,] -0.1730381 1.0118988
[15,] -0.1552507 0.9641413
[16,] -0.1820366 1.0249481
[17,] -0.1379366 0.9518739
[18,] -0.1804744 1.0215438
[19,] -0.1596881 0.9879221
[20,] -0.1551352 0.9623821
[21,] -0.1487741 0.9924152
[22,] -0.1818460 1.0203085
[23,] -0.1390505 0.9452565
[24,] -0.1709407 1.0155853
[25,] -0.1615616 0.9701107
[26,] -0.1732873 1.0139951
[27,] -0.1584225 0.9845009
[28,] -0.1734871 0.9899266
[29,] -0.1499159 0.9979010
[30,] -0.1640850 1.0128128
[31,] -0.1584035 0.9897784
[32,] -0.1597918 0.9626873
[33,] -0.1713458 0.9876645
[34,] -0.1720940 1.0101869
[35,] -0.1561971 0.9963491
[36,] -0.1598678 0.9880583
[37,] -0.1959328 1.0326375
[38,] -0.1707688 0.9805662
[39,] -0.1730277 1.0205506
[40,] -0.1546160 0.9629526
[41,] -0.1609785 1.0096706
[42,] -0.1430278 0.9791670
[43,] -0.1481606 0.9704052
[44,] -0.1812934 1.0069203
[45,] -0.1624797 0.9954147
[46,] -0.2263972 1.1074251
[47,] -0.1460128 0.9668403
[48,] -0.1727529 0.9936889
[49,] -0.1551878 0.9793975
[50,] -0.1704082 0.9901274
[51,] -0.1322900 0.9406920
[52,] -0.1494835 1.0049753
[53,] -0.1631515 1.0072997
[54,] -0.1538023 0.9660115
[55,] -0.1730536 1.0106522
[56,] -0.1715305 1.0217686
[57,] -0.1738781 1.0340199
[58,] -0.1724760 1.0008378
[59,] -0.1393797 0.9725650
[60,] -0.1797192 1.0191456
[61,] -0.1609190 0.9752423
[62,] -0.1756820 1.0313139
[63,] -0.2147338 1.0747649
[64,] -0.1700265 1.0148409
[65,] -0.1890362 1.0486265
[66,] -0.1830241 1.0085895
[67,] -0.1742902 1.0161591
[68,] -0.1240727 0.8975975
[69,] -0.1510721 0.9566539
[70,] -0.1506778 0.9852273
[71,] -0.1697857 1.0207411
[72,] -0.1592230 1.0033666
[73,] -0.1783334 1.0296205
[74,] -0.1545865 0.9922272
[75,] -0.1592670 0.9836079
[76,] -0.1492947 0.9775454
[77,] -0.1817262 1.0356666
[78,] -0.1405081 0.9463266
[79,] -0.1802573 1.0244577
[80,] -0.2008736 1.0651887
[81,] -0.1444640 0.9915624
[82,] -0.2157661 1.0890302
[83,] -0.1969575 1.0552697
[84,] -0.1751485 1.0199630
[85,] -0.1739127 0.9967420
[86,] -0.1419502 0.9484813
[87,] -0.1914078 1.0264140
[88,] -0.1745678 0.9988856
[89,] -0.1574870 0.9861215
[90,] -0.1776541 1.0421064
[91,] -0.1650321 0.9969632
[92,] -0.1805436 1.0251750
[93,] -0.1774267 0.9925020
[94,] -0.1684783 1.0034823
[95,] -0.1622454 0.9629651
[96,] -0.1583735 0.9747504
[97,] -0.1475453 0.9814714
[98,] -0.1631432 0.9853327
[99,] -0.1974697 1.0387027
[100,] -0.1506777 0.9935551
[101,] -0.1973696 1.0532105
[102,] -0.1854300 1.0202853
[103,] -0.1743934 1.0070743
[104,] -0.1907374 1.0259785
[105,] -0.2079500 1.0360323
[106,] -0.1643661 1.0091753
[107,] -0.2026129 1.0608377
[108,] -0.1839888 1.0241692
[109,] -0.1700652 1.0326750
[110,] -0.1778231 1.0074247
[111,] -0.1634512 1.0011191
[112,] -0.1633072 1.0092457
[113,] -0.1804383 1.0267848
[114,] -0.1573277 1.0066673
[115,] -0.1345778 0.9275003
[116,] -0.1950365 1.0409511
[117,] -0.1761704 1.0138517
[118,] -0.1529808 0.9970803
[119,] -0.1386321 0.9238803
[120,] -0.1541518 0.9836478
[121,] -0.1775055 1.0246489
[122,] -0.1922580 1.0568006
[123,] -0.1779449 0.9919571
[124,] -0.1845176 1.0219276
[125,] -0.2156581 1.0853025
[126,] -0.1491147 0.9495424
[127,] -0.1551748 0.9757274
[128,] -0.1892170 1.0467927
[129,] -0.1430404 0.9542750
[130,] -0.1580013 0.9779809
[131,] -0.1438539 0.9703157
[132,] -0.1692766 1.0189915
[133,] -0.1693396 1.0114952
[134,] -0.1798591 1.0212778
[135,] -0.1964096 1.0509122
[136,] -0.1728542 1.0378895
[137,] -0.2090140 1.0760444
[138,] -0.1570607 1.0068291
[139,] -0.1733614 0.9977447
[140,] -0.1696596 0.9795989
[141,] -0.1580316 0.9790548
[142,] -0.1799208 1.0134743
[143,] -0.1445422 0.9518618
[144,] -0.1649267 0.9938346
[145,] -0.1725723 1.0238495
[146,] -0.1599091 0.9665131
[147,] -0.1923726 1.0330380
[148,] -0.1973959 1.0584268
[149,] -0.1463507 0.9644216
[150,] -0.1679247 1.0089701
[151,] -0.1750804 1.0313828
[152,] -0.1957230 1.0514504
[153,] -0.1673706 1.0119983
[154,] -0.1682516 1.0134721
[155,] -0.1671656 1.0050093
[156,] -0.1485667 0.9525622
[157,] -0.2018525 1.0410615
[158,] -0.2128565 1.0654944
[159,] -0.1935343 1.0306762
[160,] -0.1367284 0.9428695
[161,] -0.1406401 0.9776211
[162,] -0.1925020 1.0358385
[163,] -0.1666279 0.9908879
[164,] -0.1813802 1.0133285
[165,] -0.1500137 0.9724187
[166,] -0.1298679 0.9225217
[167,] -0.1830164 1.0301854
[168,] -0.1361425 0.9660179
[169,] -0.1786530 1.0037611
[170,] -0.1763439 1.0056544
[171,] -0.1847810 1.0225125
[172,] -0.1633224 0.9790834
[173,] -0.1632595 1.0048817
[174,] -0.1521565 0.9691901
[175,] -0.1501240 0.9641523
[176,] -0.1852384 1.0315249
[177,] -0.1447913 0.9302012
[178,] -0.1876313 1.0383718
[179,] -0.1658932 0.9864247
[180,] -0.1329441 0.9498161
[181,] -0.1747157 1.0154394
[182,] -0.1719564 1.0062216
[183,] -0.1721170 0.9974692
[184,] -0.1677693 1.0176596
[185,] -0.1698480 1.0130385
[186,] -0.2131021 1.1038004
[187,] -0.1520521 0.9524128
[188,] -0.2064924 1.0603008
[189,] -0.1682670 0.9910281
[190,] -0.1705248 1.0121078
[191,] -0.1545912 0.9830719
[192,] -0.1659990 0.9808501
[193,] -0.1653286 1.0106849
[194,] -0.1564038 0.9819012
[195,] -0.1576622 0.9910821
[196,] -0.1663288 1.0007883
[197,] -0.1251622 0.9413586
[198,] -0.1749056 1.0259633
[199,] -0.1726707 1.0073847
[200,] -0.1743689 1.0287916
[201,] -0.1763904 1.0105388
[202,] -0.1485123 1.0033058
[203,] -0.2117403 1.0559125
[204,] -0.1680369 1.0022455
[205,] -0.1844290 1.0293421
[206,] -0.1733969 1.0131757
[207,] -0.1232361 0.9085716
[208,] -0.1835077 0.9984445
[209,] -0.1801353 1.0461562
[210,] -0.1874809 1.0410110
[211,] -0.1512918 0.9598340
[212,] -0.1717485 1.0119172
[213,] -0.1693144 1.0184664
[214,] -0.1576858 0.9814377
[215,] -0.1555694 0.9852405
[216,] -0.1720713 0.9953904
[217,] -0.1549881 0.9673649
[218,] -0.1771679 1.0256871
[219,] -0.1211022 0.9105356
[220,] -0.1303083 0.9353758
[221,] -0.1632698 1.0045698
[222,] -0.1463544 0.9706859
[223,] -0.1446694 0.9729244
[224,] -0.1507870 0.9649947
[225,] -0.1860260 1.0327242
[226,] -0.1714667 1.0052976
[227,] -0.1607564 0.9804749
[228,] -0.1787528 1.0006837
[229,] -0.1565934 0.9884775
[230,] -0.1570377 0.9678156
[231,] -0.1596805 1.0008489
[232,] -0.1663957 1.0274998
[233,] -0.1454704 0.9364282
[234,] -0.1803635 1.0212843
[235,] -0.1781276 1.0155589
[236,] -0.1786070 1.0281397
[237,] -0.1460048 0.9497290
[238,] -0.1627864 0.9700011
[239,] -0.1625018 0.9903388
[240,] -0.1724135 0.9858393
[241,] -0.1884628 1.0240039
[242,] -0.1392754 0.9426642
[243,] -0.1910326 1.0432209
[244,] -0.1653891 0.9642670
[245,] -0.1766557 1.0069076
[246,] -0.1396503 0.9443030
[247,] -0.1747318 1.0180222
[248,] -0.1629340 0.9904048
[249,] -0.1586271 0.9946838
[250,] -0.1374020 0.9343580
[251,] -0.1337354 0.9228731
[252,] -0.1720418 1.0191555
[253,] -0.1607660 1.0019473
[254,] -0.1470943 0.9869176
[255,] -0.2036385 1.0454900
[256,] -0.1462811 0.9548304
[257,] -0.1741273 1.0304742
[258,] -0.1212441 0.9203724
[259,] -0.1646721 0.9912321
[260,] -0.2193445 1.0931664
[261,] -0.1680506 1.0227414
[262,] -0.1726858 1.0149215
[263,] -0.1964757 1.0567797
[264,] -0.1370500 0.9263424
[265,] -0.1604476 0.9962605
[266,] -0.1697485 1.0204291
[267,] -0.1757017 1.0036071
[268,] -0.1505578 0.9588509
[269,] -0.1776712 1.0317416
[270,] -0.1936083 1.0560750
[271,] -0.1662493 0.9846882
[272,] -0.1608127 0.9574892
[273,] -0.1557933 0.9761793
[274,] -0.1529221 0.9815921
[275,] -0.1717047 0.9917627
[276,] -0.1696310 0.9890217
[277,] -0.1680761 0.9969446
[278,] -0.1610546 0.9719813
[279,] -0.2044580 1.0539898
[280,] -0.1578984 0.9772140
[281,] -0.1583088 0.9931033
[282,] -0.1992136 1.0471801
[283,] -0.1874156 1.0328504
[284,] -0.1398905 0.9204460
[285,] -0.1753104 0.9916116
[286,] -0.1343638 0.9326845
[287,] -0.1538998 1.0060365
[288,] -0.1760144 1.0207676
[289,] -0.1388620 0.9637450
[290,] -0.1816857 1.0328560
[291,] -0.1687266 1.0156244
[292,] -0.1766941 1.0460703
[293,] -0.1527780 0.9473203
[294,] -0.1658256 0.9693212
[295,] -0.1622672 1.0045611
[296,] -0.1426372 0.9485901
[297,] -0.1674830 1.0046266
[298,] -0.1790086 1.0198079
[299,] -0.1397103 0.9316240
[300,] -0.1410791 0.9538880
[301,] -0.1520688 0.9678901
[302,] -0.1899214 1.0290082
[303,] -0.1504792 0.9637337
[304,] -0.1643493 1.0011869
[305,] -0.1331099 0.9419335
[306,] -0.1563723 0.9764814
[307,] -0.1628858 1.0001923
[308,] -0.1667569 0.9915934
[309,] -0.1529791 0.9741474
[310,] -0.1640690 1.0023149
[311,] -0.1972968 1.0506719
[312,] -0.2055455 1.0644095
[313,] -0.1472489 0.9832079
[314,] -0.1749494 1.0105527
[315,] -0.1460915 0.9906040
[316,] -0.1796034 1.0252346
[317,] -0.1863635 1.0323918
[318,] -0.2013777 1.0461774
[319,] -0.1608490 0.9924077
[320,] -0.1871862 1.0209730
[321,] -0.1799796 1.0290107
[322,] -0.1616459 0.9746576
[323,] -0.1365747 0.9443577
[324,] -0.1481246 0.9841136
[325,] -0.1764505 1.0284868
[326,] -0.2124155 1.0843911
[327,] -0.1631815 1.0070212
[328,] -0.1674173 0.9951164
[329,] -0.1839151 1.0392863
[330,] -0.1775244 0.9911864
[331,] -0.1534663 0.9559287
[332,] -0.1761140 1.0194389
[333,] -0.1493893 0.9898809
[334,] -0.1400167 0.9638405
[335,] -0.1544377 0.9882799
[336,] -0.1735703 1.0059490
[337,] -0.1626174 1.0025301
[338,] -0.1581419 0.9861419
[339,] -0.1730115 1.0124530
[340,] -0.1563788 0.9949382
[341,] -0.1752076 1.0172927
[342,] -0.1456022 0.9772894
[343,] -0.1458178 0.9463383
[344,] -0.1617022 0.9958572
[345,] -0.1934703 1.0433425
[346,] -0.1747770 0.9896024
[347,] -0.1639795 0.9949930
[348,] -0.1678332 1.0100608
[349,] -0.1852163 1.0114238
[350,] -0.1538768 0.9834078
[351,] -0.1353845 0.9513650
[352,] -0.1491467 0.9798387
[353,] -0.1538934 0.9834331
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[833,] -0.1452499 0.9690060
[834,] -0.1912204 1.0254658
[835,] -0.1800559 1.0091060
[836,] -0.1778441 1.0300128
[837,] -0.1811142 1.0332075
[838,] -0.1624216 0.9931996
[839,] -0.1731638 0.9761660
[840,] -0.1602737 0.9564707
[841,] -0.1753463 1.0081394
[842,] -0.1406723 0.9695324
[843,] -0.1789439 1.0020023
[844,] -0.1630913 0.9970695
[845,] -0.1752290 0.9999347
[846,] -0.1622860 0.9890234
[847,] -0.1842694 1.0110108
[848,] -0.1720268 0.9939975
[849,] -0.1738113 1.0088941
[850,] -0.2054332 1.0772987
[851,] -0.1732703 1.0133332
[852,] -0.1848207 1.0306298
[853,] -0.1688346 1.0205498
[854,] -0.1505759 0.9703343
[855,] -0.1735229 1.0295333
[856,] -0.1869735 1.0433806
[857,] -0.1764856 1.0062419
[858,] -0.1536178 1.0033897
[859,] -0.1718611 0.9955814
[860,] -0.1348844 0.9437839
[861,] -0.1892973 1.0193578
[862,] -0.1882183 1.0286911
[863,] -0.1715716 1.0047731
[864,] -0.1806253 1.0267766
[865,] -0.1694987 0.9915604
[866,] -0.1516368 0.9541116
[867,] -0.1750902 1.0185156
[868,] -0.1675485 1.0070588
[869,] -0.1386680 0.9501183
[870,] -0.1756657 1.0235620
[871,] -0.1666412 1.0029049
[872,] -0.1611926 1.0265492
[873,] -0.1634887 0.9804824
[874,] -0.1728598 1.0163720
[875,] -0.1161671 0.8971733
[876,] -0.1672444 0.9952969
[877,] -0.1719615 1.0070991
[878,] -0.1591452 1.0120340
[879,] -0.1352738 0.9641847
[880,] -0.1961992 1.0380459
[881,] -0.1721523 1.0142950
[882,] -0.1692813 1.0252897
[883,] -0.2005558 1.0516790
[884,] -0.1582444 0.9565389
[885,] -0.1908112 1.0369241
[886,] -0.1556667 0.9936260
[887,] -0.1470472 0.9454042
[888,] -0.2047328 1.0507258
[889,] -0.1515883 0.9789401
[890,] -0.1622987 0.9880549
[891,] -0.1600290 1.0129990
[892,] -0.1532964 0.9740795
[893,] -0.1667343 0.9814003
[894,] -0.1743407 1.0059649
[895,] -0.1597287 1.0041655
[896,] -0.1598353 0.9577908
[897,] -0.1747722 1.0166803
[898,] -0.1719665 1.0172177
[899,] -0.1894487 1.0339012
[900,] -0.1760002 1.0206094
[901,] -0.1765603 1.0003902
[902,] -0.1658552 1.0151482
[903,] -0.1500426 0.9729887
[904,] -0.1674547 1.0207010
[905,] -0.1760547 1.0151896
[906,] -0.1523639 0.9793935
[907,] -0.1750210 1.0191295
[908,] -0.1653355 1.0006676
[909,] -0.1786037 1.0285421
[910,] -0.1435760 0.9549144
[911,] -0.1658090 0.9870342
[912,] -0.1916508 1.0380478
[913,] -0.1565003 0.9805763
[914,] -0.1763433 1.0286954
[915,] -0.2367715 1.0984673
[916,] -0.1982123 1.0457465
[917,] -0.1697756 1.0029979
[918,] -0.1836452 1.0334605
[919,] -0.1726370 1.0330784
[920,] -0.1683219 1.0121307
[921,] -0.1796113 1.0171441
[922,] -0.1809396 1.0491079
[923,] -0.1945712 1.0215810
[924,] -0.1506410 0.9826792
[925,] -0.1800323 1.0367853
[926,] -0.1646551 1.0000640
[927,] -0.1559406 0.9898952
[928,] -0.1659323 1.0084276
[929,] -0.1593027 0.9883255
[930,] -0.1611286 0.9848828
[931,] -0.1484368 0.9611656
[932,] -0.1907006 1.0490519
[933,] -0.1735598 0.9850736
[934,] -0.1532961 0.9565456
[935,] -0.1874186 1.0352017
[936,] -0.1784458 1.0178469
[937,] -0.1751489 1.0095368
[938,] -0.1433234 0.9663845
[939,] -0.2081658 1.0826374
[940,] -0.1976953 1.0388597
[941,] -0.2006691 1.0424814
[942,] -0.1713905 0.9848923
[943,] -0.1579937 0.9845753
[944,] -0.1590341 0.9805592
[945,] -0.1624735 0.9972820
[946,] -0.1548385 0.9607173
[947,] -0.1490660 0.9653262
[948,] -0.1989202 1.0552705
[949,] -0.1568205 0.9723116
[950,] -0.1759609 1.0113120
[951,] -0.1549532 1.0071352
[952,] -0.1699052 1.0203925
[953,] -0.1299368 0.9368096
[954,] -0.1606578 0.9957644
[955,] -0.1700132 0.9745825
[956,] -0.1474418 0.9532069
[957,] -0.1648604 0.9976720
[958,] -0.1561832 0.9625276
[959,] -0.1692921 1.0117697
[960,] -0.1860920 1.0244146
[961,] -0.1843421 1.0329883
[962,] -0.1515894 0.9918073
[963,] -0.1714614 1.0269564
[964,] -0.1610199 1.0032958
[965,] -0.1682890 1.0271230
[966,] -0.1644756 1.0035257
[967,] -0.1600014 0.9744283
[968,] -0.2012037 1.0664731
[969,] -0.1527193 0.9848182
[970,] -0.1678397 0.9946171
[971,] -0.1437448 0.9350025
[972,] -0.1550885 0.9646264
[973,] -0.1694720 0.9833348
[974,] -0.1722868 1.0134666
[975,] -0.1311282 0.9359723
[976,] -0.1710689 0.9888027
[977,] -0.1860245 1.0053996
[978,] -0.1520098 0.9745218
[979,] -0.1393123 0.9583837
[980,] -0.1550963 0.9735025
[981,] -0.1686412 1.0256554
[982,] -0.1683808 1.0051600
[983,] -0.2038087 1.0597734
[984,] -0.1556640 0.9724131
[985,] -0.1518065 0.9794142
[986,] -0.1318841 0.9790193
[987,] -0.1602138 1.0004644
[988,] -0.1816916 1.0370025
[989,] -0.1794502 1.0468634
[990,] -0.1637645 0.9923290
[991,] -0.1704909 0.9907060
[992,] -0.1313033 0.9166676
[993,] -0.1597615 0.9924357
[994,] -0.1855906 1.0558936
[995,] -0.1635394 1.0259573
[996,] -0.1654512 0.9871150
[997,] -0.1473220 0.9665995
[998,] -0.1629013 1.0051578
[999,] -0.1484551 0.9735056
[1000,] -0.1589381 0.9996720
$vcov
$vcov[[1]]
(Intercept) x
(Intercept) 0.0002450162 -0.0003571999
x -0.0003571999 0.0007101622
$vcov[[2]]
(Intercept) x
(Intercept) 0.0002101647 -0.0003215567
x -0.0003215567 0.0006591549
$vcov[[3]]
(Intercept) x
(Intercept) 0.0002179332 -0.0003286406
x -0.0003286406 0.0006650377
$vcov[[4]]
(Intercept) x
(Intercept) 0.0002243474 -0.0003426187
x -0.0003426187 0.0007126448
$vcov[[5]]
(Intercept) x
(Intercept) 0.0002424802 -0.0003616203
x -0.0003616203 0.0007216100
$vcov[[6]]
(Intercept) x
(Intercept) 0.0002018983 -0.0003285588
x -0.0003285588 0.0007254109
$vcov[[7]]
(Intercept) x
(Intercept) 0.0002418026 -0.0003476748
x -0.0003476748 0.0006596267
$vcov[[8]]
(Intercept) x
(Intercept) 0.0002539583 -0.0003714388
x -0.0003714388 0.0007134345
$vcov[[9]]
(Intercept) x
(Intercept) 0.000236378 -0.0003467000
x -0.000346700 0.0006871777
$vcov[[10]]
(Intercept) x
(Intercept) 0.0002281523 -0.0003493466
x -0.0003493466 0.0007117159
$vcov[[11]]
(Intercept) x
(Intercept) 0.0001860037 -0.0002866660
x -0.0002866660 0.0005870313
$vcov[[12]]
(Intercept) x
(Intercept) 0.0001934365 -0.0003160700
x -0.0003160700 0.0006875627
$vcov[[13]]
(Intercept) x
(Intercept) 0.0002374079 -0.0003455608
x -0.0003455608 0.0006967372
$vcov[[14]]
(Intercept) x
(Intercept) 0.0001993149 -0.0003017607
x -0.0003017607 0.0006219343
$vcov[[15]]
(Intercept) x
(Intercept) 0.0002088154 -0.0003303078
x -0.0003303078 0.0007030159
$vcov[[16]]
(Intercept) x
(Intercept) 0.0001985756 -0.0003047744
x -0.0003047744 0.0006298834
$vcov[[17]]
(Intercept) x
(Intercept) 0.0001786153 -0.0002802310
x -0.0002802310 0.0006402416
$vcov[[18]]
(Intercept) x
(Intercept) 0.0001911901 -0.0002959856
x -0.0002959856 0.0006142449
$vcov[[19]]
(Intercept) x
(Intercept) 0.0002123219 -0.0003271442
x -0.0003271442 0.0006854389
$vcov[[20]]
(Intercept) x
(Intercept) 0.0001978822 -0.0003179431
x -0.0003179431 0.0006909555
$vcov[[21]]
(Intercept) x
(Intercept) 0.0002382875 -0.0003540322
x -0.0003540322 0.0007567870
$vcov[[22]]
(Intercept) x
(Intercept) 0.0002573581 -0.0003869010
x -0.0003869010 0.0007538442
$vcov[[23]]
(Intercept) x
(Intercept) 0.0001808243 -0.0002899308
x -0.0002899308 0.0006639026
$vcov[[24]]
(Intercept) x
(Intercept) 0.0002280476 -0.0003344769
x -0.0003344769 0.0006520818
$vcov[[25]]
(Intercept) x
(Intercept) 0.0001923447 -0.0003103562
x -0.0003103562 0.0006683000
$vcov[[26]]
(Intercept) x
(Intercept) 0.0002503819 -0.0003698259
x -0.0003698259 0.0007203578
$vcov[[27]]
(Intercept) x
(Intercept) 0.0002131530 -0.0003224128
x -0.0003224128 0.0006617047
$vcov[[28]]
(Intercept) x
(Intercept) 0.0001758063 -0.0002865502
x -0.0002865502 0.0006190637
$vcov[[29]]
(Intercept) x
(Intercept) 0.0002368937 -0.0003380764
x -0.0003380764 0.0006633968
$vcov[[30]]
(Intercept) x
(Intercept) 0.0002359442 -0.0003479580
x -0.0003479580 0.0007011781
$vcov[[31]]
(Intercept) x
(Intercept) 0.0002225926 -0.0003473768
x -0.0003473768 0.0007579507
$vcov[[32]]
(Intercept) x
(Intercept) 0.0002014779 -0.0003033437
x -0.0003033437 0.0005656145
$vcov[[33]]
(Intercept) x
(Intercept) 0.0002259112 -0.0003459837
x -0.0003459837 0.0006804181
$vcov[[34]]
(Intercept) x
(Intercept) 0.0002007661 -0.0003037831
x -0.0003037831 0.0006177833
$vcov[[35]]
(Intercept) x
(Intercept) 0.0002399043 -0.0003434288
x -0.0003434288 0.0006616459
$vcov[[36]]
(Intercept) x
(Intercept) 0.0002257102 -0.0003377113
x -0.0003377113 0.0006720374
$vcov[[37]]
(Intercept) x
(Intercept) 0.0002493569 -0.0003866623
x -0.0003866623 0.0007669480
$vcov[[38]]
(Intercept) x
(Intercept) 0.0002575960 -0.0003989763
x -0.0003989763 0.0007887240
$vcov[[39]]
(Intercept) x
(Intercept) 0.0002171891 -0.0003219332
x -0.0003219332 0.0006561724
$vcov[[40]]
(Intercept) x
(Intercept) 0.0002361582 -0.0003686105
x -0.0003686105 0.0007621286
$vcov[[41]]
(Intercept) x
(Intercept) 0.0002308098 -0.0003412070
x -0.0003412070 0.0007019272
$vcov[[42]]
(Intercept) x
(Intercept) 0.0002314122 -0.0003244172
x -0.0003244172 0.0005983842
$vcov[[43]]
(Intercept) x
(Intercept) 0.0002205026 -0.0003343660
x -0.0003343660 0.0007098778
$vcov[[44]]
(Intercept) x
(Intercept) 0.0002146571 -0.0003312574
x -0.0003312574 0.0006543200
$vcov[[45]]
(Intercept) x
(Intercept) 0.0002226960 -0.0003324958
x -0.0003324958 0.0006618336
$vcov[[46]]
(Intercept) x
(Intercept) 0.0002981846 -0.0004091152
x -0.0004091152 0.0006849014
$vcov[[47]]
(Intercept) x
(Intercept) 0.0002483760 -0.0003613474
x -0.0003613474 0.0006912999
$vcov[[48]]
(Intercept) x
(Intercept) 0.0002381058 -0.0003597257
x -0.0003597257 0.0006968654
$vcov[[49]]
(Intercept) x
(Intercept) 0.0002052974 -0.0003199494
x -0.0003199494 0.0006912629
$vcov[[50]]
(Intercept) x
(Intercept) 0.0002125383 -0.0003427123
x -0.0003427123 0.0007469749
$vcov[[51]]
(Intercept) x
(Intercept) 0.0001617536 -0.0002552243
x -0.0002552243 0.0005980651
$vcov[[52]]
(Intercept) x
(Intercept) 0.0002059365 -0.0002966340
x -0.0002966340 0.0006124327
$vcov[[53]]
(Intercept) x
(Intercept) 0.0002257743 -0.0003243365
x -0.0003243365 0.0006142709
$vcov[[54]]
(Intercept) x
(Intercept) 0.0001983986 -0.0003065649
x -0.0003065649 0.0006387635
$vcov[[55]]
(Intercept) x
(Intercept) 0.0002245108 -0.0003357579
x -0.0003357579 0.0006660109
$vcov[[56]]
(Intercept) x
(Intercept) 0.0002329098 -0.0003292142
x -0.0003292142 0.0006039095
$vcov[[57]]
(Intercept) x
(Intercept) 0.0002459754 -0.0003454338
x -0.0003454338 0.0006375625
$vcov[[58]]
(Intercept) x
(Intercept) 0.0002033512 -0.0003122884
x -0.0003122884 0.0006302340
$vcov[[59]]
(Intercept) x
(Intercept) 0.0002436110 -0.0003567121
x -0.0003567121 0.0007375679
$vcov[[60]]
(Intercept) x
(Intercept) 0.0002126954 -0.0003261601
x -0.0003261601 0.0006706732
$vcov[[61]]
(Intercept) x
(Intercept) 0.0002201584 -0.0003344318
x -0.0003344318 0.0006557701
$vcov[[62]]
(Intercept) x
(Intercept) 0.0002353309 -0.0003429726
x -0.0003429726 0.0006707653
$vcov[[63]]
(Intercept) x
(Intercept) 0.0003099999 -0.0004394909
x -0.0004394909 0.0007577738
$vcov[[64]]
(Intercept) x
(Intercept) 0.0002424217 -0.0003531893
x -0.0003531893 0.0006808625
$vcov[[65]]
(Intercept) x
(Intercept) 0.0002649939 -0.0003753590
x -0.0003753590 0.0006745251
$vcov[[66]]
(Intercept) x
(Intercept) 0.0002117032 -0.0003223112
x -0.0003223112 0.0006174587
$vcov[[67]]
(Intercept) x
(Intercept) 0.0002859667 -0.0004025747
x -0.0004025747 0.0007074014
$vcov[[68]]
(Intercept) x
(Intercept) 0.0001885618 -0.0003048759
x -0.0003048759 0.0006873029
$vcov[[69]]
(Intercept) x
(Intercept) 0.0002286301 -0.0003573321
x -0.0003573321 0.0007436468
$vcov[[70]]
(Intercept) x
(Intercept) 0.0002192830 -0.0003248851
x -0.0003248851 0.0006704198
$vcov[[71]]
(Intercept) x
(Intercept) 0.0002572365 -0.0003644810
x -0.0003644810 0.0006722963
$vcov[[72]]
(Intercept) x
(Intercept) 0.0002060473 -0.0003020002
x -0.0003020002 0.0006111266
$vcov[[73]]
(Intercept) x
(Intercept) 0.0002454201 -0.0003747027
x -0.0003747027 0.0007788887
$vcov[[74]]
(Intercept) x
(Intercept) 0.0001887984 -0.0002827344
x -0.0002827344 0.0005903475
$vcov[[75]]
(Intercept) x
(Intercept) 0.0002351497 -0.0003496724
x -0.0003496724 0.0006806999
$vcov[[76]]
(Intercept) x
(Intercept) 0.0002422317 -0.0003597231
x -0.0003597231 0.0007344001
$vcov[[77]]
(Intercept) x
(Intercept) 0.0002405540 -0.0003502157
x -0.0003502157 0.0006757874
$vcov[[78]]
(Intercept) x
(Intercept) 0.0001827395 -0.0002862686
x -0.0002862686 0.0006332658
$vcov[[79]]
(Intercept) x
(Intercept) 0.0002105760 -0.0003132416
x -0.0003132416 0.0006121368
$vcov[[80]]
(Intercept) x
(Intercept) 0.0002519315 -0.0003602858
x -0.0003602858 0.0006545508
$vcov[[81]]
(Intercept) x
(Intercept) 0.0001990903 -0.0002869886
x -0.0002869886 0.0005908917
$vcov[[82]]
(Intercept) x
(Intercept) 0.0002867552 -0.0004018213
x -0.0004018213 0.0006944530
$vcov[[83]]
(Intercept) x
(Intercept) 0.0002592180 -0.0003728457
x -0.0003728457 0.0006803025
$vcov[[84]]
(Intercept) x
(Intercept) 0.0002338355 -0.0003465234
x -0.0003465234 0.0006818156
$vcov[[85]]
(Intercept) x
(Intercept) 0.0002573630 -0.0003908159
x -0.0003908159 0.0007643443
$vcov[[86]]
(Intercept) x
(Intercept) 0.0002002175 -0.0003098824
x -0.0003098824 0.0006583925
$vcov[[87]]
(Intercept) x
(Intercept) 0.0002299773 -0.0003551953
x -0.0003551953 0.0007036858
$vcov[[88]]
(Intercept) x
(Intercept) 0.0002477108 -0.0003821360
x -0.0003821360 0.0007661519
$vcov[[89]]
(Intercept) x
(Intercept) 0.0002257071 -0.0003448587
x -0.0003448587 0.0007245721
$vcov[[90]]
(Intercept) x
(Intercept) 0.0002269427 -0.0003154283
x -0.0003154283 0.0005756842
$vcov[[91]]
(Intercept) x
(Intercept) 0.0001738461 -0.0002639630
x -0.0002639630 0.0005422297
$vcov[[92]]
(Intercept) x
(Intercept) 0.0002445909 -0.0003554919
x -0.0003554919 0.0006619345
$vcov[[93]]
(Intercept) x
(Intercept) 0.0001817574 -0.0002944620
x -0.0002944620 0.0006208995
$vcov[[94]]
(Intercept) x
(Intercept) 0.0002562979 -0.0003865247
x -0.0003865247 0.0007755101
$vcov[[95]]
(Intercept) x
(Intercept) 0.0002214488 -0.0003517722
x -0.0003517722 0.0007276381
$vcov[[96]]
(Intercept) x
(Intercept) 0.0002200205 -0.0003458114
x -0.0003458114 0.0007415592
$vcov[[97]]
(Intercept) x
(Intercept) 0.0001703775 -0.0002556548
x -0.0002556548 0.0005466312
$vcov[[98]]
(Intercept) x
(Intercept) 0.0002144528 -0.0003307649
x -0.0003307649 0.0006854330
$vcov[[99]]
(Intercept) x
(Intercept) 0.0002755283 -0.0004134961
x -0.0004134961 0.0007874229
$vcov[[100]]
(Intercept) x
(Intercept) 0.0002462220 -0.0003641745
x -0.0003641745 0.0007608431
$vcov[[101]]
(Intercept) x
(Intercept) 0.0002894883 -0.0004282568
x -0.0004282568 0.0008199671
$vcov[[102]]
(Intercept) x
(Intercept) 0.0002617580 -0.0004002256
x -0.0004002256 0.0007910493
$vcov[[103]]
(Intercept) x
(Intercept) 0.0002018273 -0.0003026911
x -0.0003026911 0.0005931943
$vcov[[104]]
(Intercept) x
(Intercept) 0.0002673874 -0.0004035133
x -0.0004035133 0.0007630534
$vcov[[105]]
(Intercept) x
(Intercept) 0.0002522805 -0.0003893157
x -0.0003893157 0.0007319531
$vcov[[106]]
(Intercept) x
(Intercept) 0.0002410740 -0.0003549662
x -0.0003549662 0.0007164527
$vcov[[107]]
(Intercept) x
(Intercept) 0.0002130826 -0.0003109011
x -0.0003109011 0.0005779572
$vcov[[108]]
(Intercept) x
(Intercept) 0.0002422422 -0.0003562611
x -0.0003562611 0.0006696448
$vcov[[109]]
(Intercept) x
(Intercept) 0.0002202304 -0.0003212298
x -0.0003212298 0.0006495960
$vcov[[110]]
(Intercept) x
(Intercept) 0.0001788101 -0.0002806163
x -0.0002806163 0.0005845040
$vcov[[111]]
(Intercept) x
(Intercept) 0.0002343651 -0.0003420091
x -0.0003420091 0.0006576039
$vcov[[112]]
(Intercept) x
(Intercept) 0.0001847849 -0.0002676011
x -0.0002676011 0.0005262390
$vcov[[113]]
(Intercept) x
(Intercept) 0.0002446286 -0.0003563524
x -0.0003563524 0.0006764532
$vcov[[114]]
(Intercept) x
(Intercept) 0.0002730768 -0.0003990804
x -0.0003990804 0.0008235303
$vcov[[115]]
(Intercept) x
(Intercept) 0.0001971983 -0.0003094724
x -0.0003094724 0.0006610469
$vcov[[116]]
(Intercept) x
(Intercept) 0.0002653922 -0.0003985997
x -0.0003985997 0.0007691242
$vcov[[117]]
(Intercept) x
(Intercept) 0.0002345479 -0.0003650334
x -0.0003650334 0.0007686095
$vcov[[118]]
(Intercept) x
(Intercept) 0.0002056989 -0.0002990698
x -0.0002990698 0.0005975572
$vcov[[119]]
(Intercept) x
(Intercept) 0.0001699568 -0.000275687
x -0.0002756870 0.000607975
$vcov[[120]]
(Intercept) x
(Intercept) 0.0001905824 -0.0002876883
x -0.0002876883 0.0005990373
$vcov[[121]]
(Intercept) x
(Intercept) 0.0002247386 -0.0003313644
x -0.0003313644 0.0006376478
$vcov[[122]]
(Intercept) x
(Intercept) 0.0002431357 -0.0003519575
x -0.0003519575 0.0006712105
$vcov[[123]]
(Intercept) x
(Intercept) 0.0002191420 -0.0003382722
x -0.0003382722 0.0006562387
$vcov[[124]]
(Intercept) x
(Intercept) 0.0002507173 -0.0003835640
x -0.0003835640 0.0007662279
$vcov[[125]]
(Intercept) x
(Intercept) 0.0002805586 -0.0003996150
x -0.0003996150 0.0007091647
$vcov[[126]]
(Intercept) x
(Intercept) 0.0002048761 -0.0003220356
x -0.0003220356 0.0006759125
$vcov[[127]]
(Intercept) x
(Intercept) 0.0002423591 -0.0003615057
x -0.0003615057 0.0007128238
$vcov[[128]]
(Intercept) x
(Intercept) 0.0002094898 -0.0003083388
x -0.0003083388 0.0005910285
$vcov[[129]]
(Intercept) x
(Intercept) 0.0001898640 -0.0002910785
x -0.0002910785 0.0006199379
$vcov[[130]]
(Intercept) x
(Intercept) 0.0001868736 -0.0002982931
x -0.0002982931 0.0006610336
$vcov[[131]]
(Intercept) x
(Intercept) 0.0001889830 -0.0002916945
x -0.0002916945 0.0006507766
$vcov[[132]]
(Intercept) x
(Intercept) 0.0002540694 -0.0003659039
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$vcov[[133]]
(Intercept) x
(Intercept) 0.0002504997 -0.0003744482
x -0.0003744482 0.0007444022
$vcov[[134]]
(Intercept) x
(Intercept) 0.0002291392 -0.0003429455
x -0.0003429455 0.0006703156
$vcov[[135]]
(Intercept) x
(Intercept) 0.0002453927 -0.0003628757
x -0.0003628757 0.0006932502
$vcov[[136]]
(Intercept) x
(Intercept) 0.0002763340 -0.0003706421
x -0.0003706421 0.0006285153
$vcov[[137]]
(Intercept) x
(Intercept) 0.0002945632 -0.0004138236
x -0.0004138236 0.0007259292
$vcov[[138]]
(Intercept) x
(Intercept) 0.0002956886 -0.0004121747
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$vcov[[139]]
(Intercept) x
(Intercept) 0.0002153086 -0.0003302475
x -0.0003302475 0.0006630350
$vcov[[140]]
(Intercept) x
(Intercept) 0.0002024908 -0.0003207979
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$vcov[[141]]
(Intercept) x
(Intercept) 0.0002090617 -0.0003292443
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$vcov[[142]]
(Intercept) x
(Intercept) 0.0001815570 -0.0002808153
x -0.0002808153 0.0005731224
$vcov[[143]]
(Intercept) x
(Intercept) 0.0002450905 -0.0003716943
x -0.0003716943 0.0007503414
$vcov[[144]]
(Intercept) x
(Intercept) 0.0002745943 -0.0004092528
x -0.0004092528 0.0007966335
$vcov[[145]]
(Intercept) x
(Intercept) 0.0002346822 -0.0003459856
x -0.0003459856 0.0006900651
$vcov[[146]]
(Intercept) x
(Intercept) 0.0001960116 -0.0003269356
x -0.0003269356 0.0007505601
$vcov[[147]]
(Intercept) x
(Intercept) 0.0001929585 -0.0002921590
x -0.0002921590 0.0005637807
$vcov[[148]]
(Intercept) x
(Intercept) 0.0002421877 -0.0003385491
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$vcov[[149]]
(Intercept) x
(Intercept) 0.0001969502 -0.0003107291
x -0.0003107291 0.0006990614
$vcov[[150]]
(Intercept) x
(Intercept) 0.0002310414 -0.0003442472
x -0.0003442472 0.0006875845
$vcov[[151]]
(Intercept) x
(Intercept) 0.0002863494 -0.0004008845
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$vcov[[152]]
(Intercept) x
(Intercept) 0.0002323150 -0.0003412499
x -0.0003412499 0.0006422814
$vcov[[153]]
(Intercept) x
(Intercept) 0.0002283363 -0.0003358974
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$vcov[[154]]
(Intercept) x
(Intercept) 0.0002505739 -0.0003622594
x -0.0003622594 0.0006896577
$vcov[[155]]
(Intercept) x
(Intercept) 0.0002123548 -0.0003230835
x -0.0003230835 0.0006680183
$vcov[[156]]
(Intercept) x
(Intercept) 0.0002036828 -0.0003126501
x -0.0003126501 0.0006321132
$vcov[[157]]
(Intercept) x
(Intercept) 0.0002262104 -0.0003474091
x -0.0003474091 0.0006739376
$vcov[[158]]
(Intercept) x
(Intercept) 0.0002809863 -0.0004042105
x -0.0004042105 0.0007042362
$vcov[[159]]
(Intercept) x
(Intercept) 0.0002481685 -0.0003857034
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$vcov[[160]]
(Intercept) x
(Intercept) 0.0002129794 -0.0003199933
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$vcov[[161]]
(Intercept) x
(Intercept) 0.0002179792 -0.0003129530
x -0.0003129530 0.0006244165
$vcov[[162]]
(Intercept) x
(Intercept) 0.0003114342 -0.0004502618
x -0.0004502618 0.0008068186
$vcov[[163]]
(Intercept) x
(Intercept) 0.0001962529 -0.0003066384
x -0.0003066384 0.0006494521
$vcov[[164]]
(Intercept) x
(Intercept) 0.0002606597 -0.0003915137
x -0.0003915137 0.0007462907
$vcov[[165]]
(Intercept) x
(Intercept) 0.0002176373 -0.0003257732
x -0.0003257732 0.0006619899
$vcov[[166]]
(Intercept) x
(Intercept) 0.0001985387 -0.0003102746
x -0.0003102746 0.0006714376
$vcov[[167]]
(Intercept) x
(Intercept) 0.0001862880 -0.0002777471
x -0.0002777471 0.0005427319
$vcov[[168]]
(Intercept) x
(Intercept) 0.0002395010 -0.0003397806
x -0.0003397806 0.0006494233
$vcov[[169]]
(Intercept) x
(Intercept) 0.0002213363 -0.0003388724
x -0.0003388724 0.0006629209
$vcov[[170]]
(Intercept) x
(Intercept) 0.0002284513 -0.0003505793
x -0.0003505793 0.0007076044
$vcov[[171]]
(Intercept) x
(Intercept) 0.0002443218 -0.0003797090
x -0.0003797090 0.0007777521
$vcov[[172]]
(Intercept) x
(Intercept) 0.0002343744 -0.0003613374
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$vcov[[173]]
(Intercept) x
(Intercept) 0.0003033504 -0.0004268975
x -0.0004268975 0.0007638461
$vcov[[174]]
(Intercept) x
(Intercept) 0.0002296356 -0.0003432833
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$vcov[[175]]
(Intercept) x
(Intercept) 0.0002314485 -0.0003586664
x -0.0003586664 0.0007578870
$vcov[[176]]
(Intercept) x
(Intercept) 0.0002317901 -0.0003510925
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$vcov[[177]]
(Intercept) x
(Intercept) 0.0001935738 -0.0003039250
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$vcov[[178]]
(Intercept) x
(Intercept) 0.0002798533 -0.0004074646
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$vcov[[179]]
(Intercept) x
(Intercept) 0.0002193156 -0.0003406798
x -0.0003406798 0.0006979933
$vcov[[180]]
(Intercept) x
(Intercept) 0.0002054939 -0.0003033064
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$vcov[[181]]
(Intercept) x
(Intercept) 0.0002256173 -0.0003438297
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$vcov[[182]]
(Intercept) x
(Intercept) 0.0002343572 -0.0003556627
x -0.0003556627 0.0007181690
$vcov[[183]]
(Intercept) x
(Intercept) 0.0002173729 -0.0003289017
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$vcov[[184]]
(Intercept) x
(Intercept) 0.0002246686 -0.0003376895
x -0.0003376895 0.0007046804
$vcov[[185]]
(Intercept) x
(Intercept) 0.000240201 -0.0003457330
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$vcov[[186]]
(Intercept) x
(Intercept) 0.0002268652 -0.0003209615
x -0.0003209615 0.0006031243
$vcov[[187]]
(Intercept) x
(Intercept) 0.0002011717 -0.0003147273
x -0.0003147273 0.0006507673
$vcov[[188]]
(Intercept) x
(Intercept) 0.0002275953 -0.0003589099
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$vcov[[189]]
(Intercept) x
(Intercept) 0.0002969248 -0.0004534419
x -0.0004534419 0.0008973571
$vcov[[190]]
(Intercept) x
(Intercept) 0.000250151 -0.0003642640
x -0.000364264 0.0006965896
$vcov[[191]]
(Intercept) x
(Intercept) 0.0002040152 -0.0003168604
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$vcov[[192]]
(Intercept) x
(Intercept) 0.0002052854 -0.0003196432
x -0.0003196432 0.0006564333
$vcov[[193]]
(Intercept) x
(Intercept) 0.0002848255 -0.0004145541
x -0.0004145541 0.0008069963
$vcov[[194]]
(Intercept) x
(Intercept) 0.0001995615 -0.0002964541
x -0.0002964541 0.0005819469
$vcov[[195]]
(Intercept) x
(Intercept) 0.0002375654 -0.0003576816
x -0.0003576816 0.0007368687
$vcov[[196]]
(Intercept) x
(Intercept) 0.0002177842 -0.0003284412
x -0.0003284412 0.0006676953
$vcov[[197]]
(Intercept) x
(Intercept) 0.0001767124 -0.0002707254
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$vcov[[198]]
(Intercept) x
(Intercept) 0.0002556934 -0.0003796756
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$vcov[[199]]
(Intercept) x
(Intercept) 0.0002785588 -0.0004085862
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$vcov[[200]]
(Intercept) x
(Intercept) 0.0002493072 -0.0003616520
x -0.0003616520 0.0006988958
$vcov[[201]]
(Intercept) x
(Intercept) 0.0002101533 -0.0003203058
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$vcov[[202]]
(Intercept) x
(Intercept) 0.0002559088 -0.0003570100
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$vcov[[203]]
(Intercept) x
(Intercept) 0.0003078538 -0.0004496294
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$vcov[[204]]
(Intercept) x
(Intercept) 0.0002470853 -0.0003651907
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$vcov[[205]]
(Intercept) x
(Intercept) 0.0002880380 -0.0004266145
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$vcov[[206]]
(Intercept) x
(Intercept) 0.0002387949 -0.0003575660
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$vcov[[207]]
(Intercept) x
(Intercept) 0.0001496387 -0.0002423873
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$vcov[[208]]
(Intercept) x
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$vcov[[209]]
(Intercept) x
(Intercept) 0.0002498519 -0.0003586102
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$vcov[[210]]
(Intercept) x
(Intercept) 0.0002496791 -0.0003620727
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$vcov[[211]]
(Intercept) x
(Intercept) 0.0002326114 -0.0003532754
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$vcov[[212]]
(Intercept) x
(Intercept) 0.0002235092 -0.0003309012
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$vcov[[213]]
(Intercept) x
(Intercept) 0.0002219025 -0.0003271557
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$vcov[[214]]
(Intercept) x
(Intercept) 0.0002189668 -0.0003366616
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$vcov[[215]]
(Intercept) x
(Intercept) 0.0002088711 -0.0003144850
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$vcov[[216]]
(Intercept) x
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$vcov[[217]]
(Intercept) x
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$vcov[[218]]
(Intercept) x
(Intercept) 0.0002585937 -0.0003775644
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$vcov[[219]]
(Intercept) x
(Intercept) 0.0001707454 -0.0002741397
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$vcov[[220]]
(Intercept) x
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$vcov[[221]]
(Intercept) x
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$vcov[[222]]
(Intercept) x
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$vcov[[223]]
(Intercept) x
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$vcov[[224]]
(Intercept) x
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$vcov[[225]]
(Intercept) x
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$vcov[[226]]
(Intercept) x
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$vcov[[227]]
(Intercept) x
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$vcov[[228]]
(Intercept) x
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$vcov[[229]]
(Intercept) x
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$vcov[[230]]
(Intercept) x
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$vcov[[231]]
(Intercept) x
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$vcov[[232]]
(Intercept) x
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$vcov[[233]]
(Intercept) x
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$vcov[[234]]
(Intercept) x
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$vcov[[235]]
(Intercept) x
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$vcov[[236]]
(Intercept) x
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$vcov[[237]]
(Intercept) x
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$vcov[[238]]
(Intercept) x
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$vcov[[239]]
(Intercept) x
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$vcov[[240]]
(Intercept) x
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$vcov[[241]]
(Intercept) x
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$vcov[[242]]
(Intercept) x
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$vcov[[243]]
(Intercept) x
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$vcov[[244]]
(Intercept) x
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$vcov[[245]]
(Intercept) x
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$vcov[[246]]
(Intercept) x
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$vcov[[247]]
(Intercept) x
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$vcov[[248]]
(Intercept) x
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$vcov[[249]]
(Intercept) x
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$vcov[[250]]
(Intercept) x
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$vcov[[251]]
(Intercept) x
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$vcov[[252]]
(Intercept) x
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$vcov[[253]]
(Intercept) x
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$vcov[[254]]
(Intercept) x
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$vcov[[255]]
(Intercept) x
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$vcov[[256]]
(Intercept) x
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$vcov[[257]]
(Intercept) x
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$vcov[[258]]
(Intercept) x
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$vcov[[259]]
(Intercept) x
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$vcov[[260]]
(Intercept) x
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$vcov[[261]]
(Intercept) x
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$vcov[[262]]
(Intercept) x
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$vcov[[263]]
(Intercept) x
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$vcov[[264]]
(Intercept) x
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$vcov[[265]]
(Intercept) x
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$vcov[[266]]
(Intercept) x
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$vcov[[267]]
(Intercept) x
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$vcov[[268]]
(Intercept) x
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$vcov[[269]]
(Intercept) x
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$vcov[[270]]
(Intercept) x
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$vcov[[271]]
(Intercept) x
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x -0.0003987085 0.0008359728
$vcov[[272]]
(Intercept) x
(Intercept) 0.0002329541 -0.0003642679
x -0.0003642679 0.0007222600
$vcov[[273]]
(Intercept) x
(Intercept) 0.0001693351 -0.0002714829
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$vcov[[274]]
(Intercept) x
(Intercept) 0.0001901461 -0.0002854116
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$vcov[[275]]
(Intercept) x
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$vcov[[276]]
(Intercept) x
(Intercept) 0.0002465245 -0.0003788548
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$vcov[[277]]
(Intercept) x
(Intercept) 0.0002599954 -0.0003992854
x -0.0003992854 0.0008230517
$vcov[[278]]
(Intercept) x
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$vcov[[279]]
(Intercept) x
(Intercept) 0.0002415629 -0.0003618028
x -0.0003618028 0.0006824951
$vcov[[280]]
(Intercept) x
(Intercept) 0.0002109317 -0.0003413683
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$vcov[[281]]
(Intercept) x
(Intercept) 0.0002503940 -0.0003772677
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$vcov[[282]]
(Intercept) x
(Intercept) 0.0002058743 -0.0003164673
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$vcov[[283]]
(Intercept) x
(Intercept) 0.0002579032 -0.0003853942
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$vcov[[284]]
(Intercept) x
(Intercept) 0.0002278892 -0.0003596030
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$vcov[[285]]
(Intercept) x
(Intercept) 0.0002094162 -0.0003288222
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$vcov[[286]]
(Intercept) x
(Intercept) 0.0001991654 -0.0003198774
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$vcov[[287]]
(Intercept) x
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$vcov[[288]]
(Intercept) x
(Intercept) 0.0002327866 -0.0003475373
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$vcov[[289]]
(Intercept) x
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$vcov[[290]]
(Intercept) x
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$vcov[[291]]
(Intercept) x
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$vcov[[292]]
(Intercept) x
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$vcov[[293]]
(Intercept) x
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$vcov[[294]]
(Intercept) x
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$vcov[[295]]
(Intercept) x
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$vcov[[296]]
(Intercept) x
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$vcov[[297]]
(Intercept) x
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$vcov[[298]]
(Intercept) x
(Intercept) 0.0002263872 -0.0003298466
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$vcov[[299]]
(Intercept) x
(Intercept) 0.0002432687 -0.0003792890
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$vcov[[300]]
(Intercept) x
(Intercept) 0.0002245073 -0.0003474876
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$vcov[[301]]
(Intercept) x
(Intercept) 0.0002106422 -0.000319863
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$vcov[[302]]
(Intercept) x
(Intercept) 0.0002250694 -0.0003404127
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$vcov[[303]]
(Intercept) x
(Intercept) 0.0002171306 -0.0003435901
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$vcov[[304]]
(Intercept) x
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$vcov[[305]]
(Intercept) x
(Intercept) 0.0001783445 -0.0002752202
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$vcov[[306]]
(Intercept) x
(Intercept) 0.0002156409 -0.0003197075
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$vcov[[307]]
(Intercept) x
(Intercept) 0.0002237123 -0.0003421217
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$vcov[[308]]
(Intercept) x
(Intercept) 0.0002113860 -0.0003342536
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$vcov[[309]]
(Intercept) x
(Intercept) 0.0001908803 -0.0002950469
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$vcov[[310]]
(Intercept) x
(Intercept) 0.0002153532 -0.0003261993
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$vcov[[311]]
(Intercept) x
(Intercept) 0.0003036383 -0.0004311371
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$vcov[[312]]
(Intercept) x
(Intercept) 0.0002645843 -0.0003839020
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$vcov[[313]]
(Intercept) x
(Intercept) 0.0002463655 -0.0003624354
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$vcov[[314]]
(Intercept) x
(Intercept) 0.0002811918 -0.0004151233
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$vcov[[315]]
(Intercept) x
(Intercept) 0.0001986534 -0.0002830829
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$vcov[[316]]
(Intercept) x
(Intercept) 0.0002672359 -0.0003993014
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$vcov[[317]]
(Intercept) x
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$vcov[[318]]
(Intercept) x
(Intercept) 0.0002341059 -0.0003437787
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$vcov[[319]]
(Intercept) x
(Intercept) 0.0002377098 -0.0003617857
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$vcov[[320]]
(Intercept) x
(Intercept) 0.0002165182 -0.0003348112
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$vcov[[321]]
(Intercept) x
(Intercept) 0.0002042377 -0.0002949315
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$vcov[[322]]
(Intercept) x
(Intercept) 0.0002625846 -0.0004152410
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$vcov[[323]]
(Intercept) x
(Intercept) 0.0002003850 -0.0003001073
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$vcov[[324]]
(Intercept) x
(Intercept) 0.0002037019 -0.0003025809
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$vcov[[325]]
(Intercept) x
(Intercept) 0.0002778805 -0.0003957398
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$vcov[[326]]
(Intercept) x
(Intercept) 0.0002287172 -0.0003313399
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$vcov[[327]]
(Intercept) x
(Intercept) 0.0002493770 -0.0003605829
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$vcov[[328]]
(Intercept) x
(Intercept) 0.0002099083 -0.0003209875
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$vcov[[329]]
(Intercept) x
(Intercept) 0.0002928401 -0.0004165228
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$vcov[[330]]
(Intercept) x
(Intercept) 0.0002672769 -0.0004265563
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$vcov[[331]]
(Intercept) x
(Intercept) 0.0002075382 -0.0003299704
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$vcov[[332]]
(Intercept) x
(Intercept) 0.0002509727 -0.0003757391
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$vcov[[333]]
(Intercept) x
(Intercept) 0.0002131916 -0.0003050025
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$vcov[[334]]
(Intercept) x
(Intercept) 0.0001938518 -0.0002908987
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$vcov[[335]]
(Intercept) x
(Intercept) 0.0001941580 -0.0002873867
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$vcov[[336]]
(Intercept) x
(Intercept) 0.0002178833 -0.0003382153
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$vcov[[337]]
(Intercept) x
(Intercept) 0.0001941106 -0.0002848092
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$vcov[[338]]
(Intercept) x
(Intercept) 0.0002802541 -0.0004022322
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$vcov[[339]]
(Intercept) x
(Intercept) 0.0002007134 -0.0003013428
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$vcov[[340]]
(Intercept) x
(Intercept) 0.0002363617 -0.0003506413
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$vcov[[341]]
(Intercept) x
(Intercept) 0.0001979170 -0.0002961681
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$vcov[[342]]
(Intercept) x
(Intercept) 0.0001931923 -0.0002935987
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$vcov[[343]]
(Intercept) x
(Intercept) 0.0002156726 -0.0003374403
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$vcov[[344]]
(Intercept) x
(Intercept) 0.0002154237 -0.0003309689
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$vcov[[345]]
(Intercept) x
(Intercept) 0.0002640832 -0.0003807280
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$vcov[[346]]
(Intercept) x
(Intercept) 0.0001730849 -0.0002800961
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$vcov[[347]]
(Intercept) x
(Intercept) 0.0002389282 -0.0003560901
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$vcov[[348]]
(Intercept) x
(Intercept) 0.000217281 -0.0003267120
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$vcov[[349]]
(Intercept) x
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$vcov[[350]]
(Intercept) x
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$vcov[[351]]
(Intercept) x
(Intercept) 0.0001758501 -0.0002750046
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$vcov[[352]]
(Intercept) x
(Intercept) 0.0001966465 -0.0002936232
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$vcov[[353]]
(Intercept) x
(Intercept) 0.0002580482 -0.0003762030
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$vcov[[354]]
(Intercept) x
(Intercept) 0.0002183939 -0.0003247516
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$vcov[[355]]
(Intercept) x
(Intercept) 0.0002476784 -0.0003692399
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$vcov[[356]]
(Intercept) x
(Intercept) 0.0002293497 -0.0003441307
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$vcov[[357]]
(Intercept) x
(Intercept) 0.0003132964 -0.0004314064
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$vcov[[358]]
(Intercept) x
(Intercept) 0.0002493328 -0.0003609936
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$vcov[[359]]
(Intercept) x
(Intercept) 0.0001957580 -0.0002877645
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$vcov[[360]]
(Intercept) x
(Intercept) 0.0002195512 -0.0003416293
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$vcov[[361]]
(Intercept) x
(Intercept) 0.0002325055 -0.0003333937
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$vcov[[362]]
(Intercept) x
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$vcov[[363]]
(Intercept) x
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$vcov[[364]]
(Intercept) x
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$vcov[[365]]
(Intercept) x
(Intercept) 0.0002071695 -0.0003093493
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$vcov[[366]]
(Intercept) x
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$vcov[[367]]
(Intercept) x
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$vcov[[368]]
(Intercept) x
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$vcov[[369]]
(Intercept) x
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$vcov[[370]]
(Intercept) x
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$vcov[[371]]
(Intercept) x
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$vcov[[372]]
(Intercept) x
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$vcov[[373]]
(Intercept) x
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$vcov[[374]]
(Intercept) x
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$vcov[[375]]
(Intercept) x
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$vcov[[376]]
(Intercept) x
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$vcov[[377]]
(Intercept) x
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$vcov[[378]]
(Intercept) x
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$vcov[[379]]
(Intercept) x
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$vcov[[380]]
(Intercept) x
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$vcov[[381]]
(Intercept) x
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$vcov[[382]]
(Intercept) x
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$vcov[[383]]
(Intercept) x
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$vcov[[384]]
(Intercept) x
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$vcov[[385]]
(Intercept) x
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$vcov[[386]]
(Intercept) x
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$vcov[[387]]
(Intercept) x
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$vcov[[388]]
(Intercept) x
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$vcov[[389]]
(Intercept) x
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$vcov[[390]]
(Intercept) x
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$vcov[[391]]
(Intercept) x
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$vcov[[392]]
(Intercept) x
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$vcov[[393]]
(Intercept) x
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$vcov[[394]]
(Intercept) x
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$vcov[[395]]
(Intercept) x
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$vcov[[396]]
(Intercept) x
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$vcov[[397]]
(Intercept) x
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$vcov[[398]]
(Intercept) x
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$vcov[[399]]
(Intercept) x
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$vcov[[400]]
(Intercept) x
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$vcov[[401]]
(Intercept) x
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$vcov[[402]]
(Intercept) x
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$vcov[[403]]
(Intercept) x
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$vcov[[404]]
(Intercept) x
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$vcov[[405]]
(Intercept) x
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$vcov[[406]]
(Intercept) x
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$vcov[[407]]
(Intercept) x
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$vcov[[408]]
(Intercept) x
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$vcov[[409]]
(Intercept) x
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$vcov[[410]]
(Intercept) x
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$vcov[[411]]
(Intercept) x
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$vcov[[412]]
(Intercept) x
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$vcov[[413]]
(Intercept) x
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$vcov[[414]]
(Intercept) x
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$vcov[[415]]
(Intercept) x
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$vcov[[416]]
(Intercept) x
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$vcov[[417]]
(Intercept) x
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$vcov[[418]]
(Intercept) x
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$vcov[[419]]
(Intercept) x
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$vcov[[420]]
(Intercept) x
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$vcov[[421]]
(Intercept) x
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$vcov[[422]]
(Intercept) x
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$vcov[[423]]
(Intercept) x
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$vcov[[424]]
(Intercept) x
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$vcov[[425]]
(Intercept) x
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$vcov[[426]]
(Intercept) x
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$vcov[[427]]
(Intercept) x
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$vcov[[428]]
(Intercept) x
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$vcov[[429]]
(Intercept) x
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$vcov[[430]]
(Intercept) x
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$vcov[[431]]
(Intercept) x
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$vcov[[432]]
(Intercept) x
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$vcov[[433]]
(Intercept) x
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$vcov[[434]]
(Intercept) x
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$vcov[[435]]
(Intercept) x
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$vcov[[436]]
(Intercept) x
(Intercept) 0.0001269631 -0.0001885109
x -0.0001885109 0.0003768984
$vcov[[437]]
(Intercept) x
(Intercept) 0.0002223616 -0.0003247020
x -0.0003247020 0.0006294647
$vcov[[438]]
(Intercept) x
(Intercept) 0.0002292925 -0.0003589568
x -0.0003589568 0.0007393253
$vcov[[439]]
(Intercept) x
(Intercept) 0.0001841753 -0.0002844396
x -0.0002844396 0.0005761496
$vcov[[440]]
(Intercept) x
(Intercept) 0.0002002375 -0.0003105999
x -0.0003105999 0.0006328221
$vcov[[441]]
(Intercept) x
(Intercept) 0.0002228916 -0.0003393547
x -0.0003393547 0.0006985994
$vcov[[442]]
(Intercept) x
(Intercept) 0.0002305385 -0.0003492654
x -0.0003492654 0.0006970479
$vcov[[443]]
(Intercept) x
(Intercept) 0.0002012718 -0.0003067735
x -0.0003067735 0.0006779497
$vcov[[444]]
(Intercept) x
(Intercept) 0.0002263644 -0.0003380990
x -0.0003380990 0.0006848969
$vcov[[445]]
(Intercept) x
(Intercept) 0.0002495402 -0.0003709652
x -0.0003709652 0.0007130506
$vcov[[446]]
(Intercept) x
(Intercept) 0.0002040580 -0.0003024111
x -0.0003024111 0.0006156315
$vcov[[447]]
(Intercept) x
(Intercept) 0.0002313398 -0.0003403708
x -0.0003403708 0.0006768344
$vcov[[448]]
(Intercept) x
(Intercept) 0.0002628344 -0.0003901726
x -0.0003901726 0.0007636650
$vcov[[449]]
(Intercept) x
(Intercept) 0.0002374043 -0.0003553257
x -0.0003553257 0.0007264850
$vcov[[450]]
(Intercept) x
(Intercept) 0.0002577622 -0.0003773709
x -0.0003773709 0.0007660970
$vcov[[451]]
(Intercept) x
(Intercept) 0.0001951805 -0.0003042165
x -0.0003042165 0.0006398132
$vcov[[452]]
(Intercept) x
(Intercept) 0.0002277238 -0.0003375663
x -0.0003375663 0.0006844174
$vcov[[453]]
(Intercept) x
(Intercept) 0.0002587649 -0.0003769840
x -0.0003769840 0.0007433968
$vcov[[454]]
(Intercept) x
(Intercept) 0.0002734106 -0.0003870717
x -0.0003870717 0.0007284970
$vcov[[455]]
(Intercept) x
(Intercept) 0.0002019914 -0.0003161633
x -0.0003161633 0.0006853421
$vcov[[456]]
(Intercept) x
(Intercept) 0.0002374001 -0.0003450583
x -0.0003450583 0.0006766674
$vcov[[457]]
(Intercept) x
(Intercept) 0.0002543128 -0.0003987869
x -0.0003987869 0.0008602529
$vcov[[458]]
(Intercept) x
(Intercept) 0.0002258773 -0.0003569869
x -0.0003569869 0.0007465080
$vcov[[459]]
(Intercept) x
(Intercept) 0.0002366540 -0.0003441812
x -0.0003441812 0.0006647091
$vcov[[460]]
(Intercept) x
(Intercept) 0.0002035013 -0.0003185106
x -0.0003185106 0.0006728174
$vcov[[461]]
(Intercept) x
(Intercept) 0.0002218515 -0.0003300805
x -0.0003300805 0.0006715531
$vcov[[462]]
(Intercept) x
(Intercept) 0.0002380754 -0.0003571419
x -0.0003571419 0.0006887302
$vcov[[463]]
(Intercept) x
(Intercept) 0.0002624198 -0.0003894131
x -0.0003894131 0.0007682959
$vcov[[464]]
(Intercept) x
(Intercept) 0.0002197255 -0.0003335626
x -0.0003335626 0.0006889783
$vcov[[465]]
(Intercept) x
(Intercept) 0.0002443082 -0.0003632190
x -0.0003632190 0.0007201162
$vcov[[466]]
(Intercept) x
(Intercept) 0.0002387058 -0.0003564625
x -0.0003564625 0.0006742334
$vcov[[467]]
(Intercept) x
(Intercept) 0.0002604429 -0.0003779215
x -0.0003779215 0.0007377255
$vcov[[468]]
(Intercept) x
(Intercept) 0.0002403186 -0.0003708556
x -0.0003708556 0.0007417527
$vcov[[469]]
(Intercept) x
(Intercept) 0.0002332533 -0.0003381550
x -0.0003381550 0.0006506476
$vcov[[470]]
(Intercept) x
(Intercept) 0.0002596600 -0.0004086151
x -0.0004086151 0.0008595212
$vcov[[471]]
(Intercept) x
(Intercept) 0.0002277268 -0.0003699862
x -0.0003699862 0.0008002428
$vcov[[472]]
(I...
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