Overview

Six models are used to forecast each major age class of sockeye salmon in the major rivers of Bristol Bay. Five of these models are linear regressions and the sixth is a 5-year running average of the age class under consideration.

Forecast models

This document covers output from five linnear regression models run against four major age classes in this river. Three regressions are variations of the sibling relationship with the age being forecast (Table 1). The first regression (sibling) uses observed forecast age and the brood year younger sibling return. The second regression (ln.sibling) uses a natural log transformation of both the forecasted age and the sibling return. The third regression (lnY.sibling) uses the sibling age return and a natural log transformation of the forecasted age. Two linnear regression models based on forecasted age return and total spawning escapment. The first of these (lnS.lnR) is the natural log of the forecasted age class regressed against the natural log of the spawning escapement. The second forecast method that relies on the relationship between the forecasted age and the spawning escapement is a linnear transformation of the Ricker relationship.

Table 1. Forecast ages and the sibling age class used for forecasting.

Forecast Age Sibling
Age.12 Age.11
Age.22 Age.21
Age.13 Age.12
Age.23 Age.22

Output

Each model output consists of a table and two graphs. The table shows the most recent 10 years of observed returns for the age being forecast (‘Observed Return’) and the relevant sibling return (‘Sibling Return’) shown in bold black text. Brood and return years are shown in blue text. Two regression model statistics (R-squared and P-value of the slope) are shown in red. Model forecasted returns are shown in bold black text with a yellow highlight. Error measurements are shown in green text. Error measurements shown are absolute deviation (AD), absolute percent error (APE), percent error (PE) and arc tan percent error (AAPE).

After the table summarizing the model output for the most recenet ten years, two graphs are shown for each of the linnear regression models. The first graph is a scatter plot of the data with a linnear regression superimposed. The second graph is a plot of the residuals of the regression analysis.

Absolute deviation (AD) is defined as

\[\ AD = O - F\] where

O = Observed Return

F = Forecasted Return

Percent error (PE) is defined as

\[\ PE = (F - O)/O\] Absolute Percent error (APE) is defined as

\[\ APE = |(F - O)/O|\]

Arctangent percent error (AAPE) is defined (Kim and Kim, 2016) as \[\ AAPE = arctan(|((O - F)/O)|)\]

At the end of the model output section for each age class, a performance table is presented that contains the mean absolute deviation (MAD), neam absolute percent error (MAPE), mean percent error (MPE) and mean arctanget percent error (MAAPE). These performance metrics are calculated and presented across the most recent three and five years. Color bars show the relative size of each metric.

age.12

Below are model outputs using data from 1972

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2008 52,672 1,054,704 -0.028 0.844 126,717 74,045 0.58 0.58 0.95
2013 2009 132,092 514,188 -0.029 0.991 115,111 16,980 0.15 -0.15 0.13
2014 2010 567,609 518,040 -0.028 0.980 115,758 451,851 3.90 -3.90 0.67
2015 2011 507,840 421,380 -0.026 0.864 121,998 385,842 3.16 -3.16 0.65
2016 2012 364,112 193,326 -0.025 0.803 120,637 243,475 2.02 -2.02 0.59
2017 2013 906,913 387,036 -0.025 0.869 129,259 777,654 6.02 -6.02 0.71
2018 2014 734,904 340,590 -0.023 0.810 134,934 599,970 4.45 -4.45 0.68
2019 2015 233,249 651,172 -0.023 0.788 147,524 85,725 0.58 -0.58 0.35
2020 2016 559,275 469,230 -0.021 0.740 146,356 412,919 2.82 -2.82 0.64
2021 2017 NA 578,700 -0.019 0.672 155,999 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2008 52,672 1,054,704 0.288 0 85,350 32,678 0.38 0.38 0.56
2013 2009 132,092 514,188 0.326 0 146,996 14,904 0.10 0.10 0.11
2014 2010 567,609 518,040 0.328 0 146,239 421,370 2.88 -2.88 0.64
2015 2011 507,840 421,380 0.314 0 156,272 351,568 2.25 -2.25 0.61
2016 2012 364,112 193,326 0.308 0 127,919 236,193 1.85 -1.85 0.58
2017 2013 906,913 387,036 0.314 0 164,791 742,122 4.50 -4.50 0.69
2018 2014 734,904 340,590 0.303 0 169,289 565,615 3.34 -3.34 0.66
2019 2015 233,249 651,172 0.299 0 155,421 77,828 0.50 -0.50 0.32
2020 2016 559,275 469,230 0.298 0 177,609 381,665 2.15 -2.15 0.60
2021 2017 NA 578,700 0.290 0 172,382 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2008 52,671.93 408,743 356,071 0.87 0.87 1.42
2013 2009 132,091.51 264,771 132,680 0.50 0.50 0.79
2014 2010 567,608.86 171,948 395,661 2.30 -2.30 0.61
2015 2011 507,839.90 220,199 287,641 1.31 -1.31 0.52
2016 2012 364,111.88 284,171 79,941 0.28 -0.28 0.22
2017 2013 906,912.97 324,865 582,048 1.79 -1.79 0.57
2018 2014 734,903.92 495,713 239,191 0.48 -0.48 0.31
2019 2015 233,249.01 616,276 383,027 0.62 0.62 1.02
2020 2016 559,274.79 549,404 9,871 0.02 -0.02 0.02
2021 2017 NA 559,691 NA NA NA NA

Performance summary

Average and ricker are performing well. Combined they forecast 393,000.

model range MAD MAPE MPE MAAPE
sibling 5 years 331,058 328.09% -328.09% 0.41
sibling 3 years 273,265 419.63% -419.63% 0.33
ln.sibling 5 years 391,819 265.30% -265.30% 0.56
ln.sibling 3 years 312,537 171.22% -171.22% 0.50
lnY.sibling 5 years 378,590 237.76% -237.76% 0.55
lnY.sibling 3 years 290,585 125.68% -125.68% 0.49
lnS.lnR 5 years 423,948 317.67% -317.67% 0.59
lnS.lnR 3 years 366,204 261.63% -261.63% 0.56
ricker 5 years 400,685 246.81% -246.81% 0.57
ricker 3 years 341,703 199.69% -199.69% 0.53
average 5 years 258,816 63.90% -39.04% 0.43
average 3 years 210,696 37.40% 4.03% 0.45

age.22

Below are model outputs using data from 1972

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 16,128 415,452 -0.016 0.500 16,210 82 0.01 0.01 0.01
2013 2008 38,397 1,054,704 -0.015 0.492 19,909 18,488 0.93 -0.93 0.45
2014 2009 56,113 514,188 -0.007 0.390 17,691 38,422 2.17 -2.17 0.60
2015 2010 500 518,040 -0.001 0.333 18,575 18,075 0.97 0.97 1.54
2016 2011 11,165 421,380 -0.016 0.533 15,471 4,307 0.28 0.28 0.37
2017 2012 4,050 193,326 -0.016 0.537 13,160 9,109 0.69 0.69 1.15
2018 2013 678 387,036 -0.013 0.482 14,732 14,054 0.95 0.95 1.52
2019 2014 5,345 340,590 -0.017 0.568 13,262 7,917 0.60 0.60 0.98
2020 2015 8,237 651,172 -0.016 0.575 14,599 6,362 0.44 0.44 0.66
2021 2016 NA 469,230 -0.017 0.608 13,471 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 16,128 415,452 0.085 0.050 20,449 4,321 0.21 0.21 0.26
2013 2008 38,397 1,054,704 0.086 0.046 20,121 18,277 0.91 -0.91 0.44
2014 2009 56,113 514,188 0.083 0.047 22,397 33,716 1.51 -1.51 0.54
2015 2010 500 518,040 0.079 0.048 23,069 22,569 0.98 0.98 1.55
2016 2011 11,165 421,380 0.077 0.049 19,323 8,159 0.42 0.42 0.63
2017 2012 4,050 193,326 0.077 0.046 12,192 8,141 0.67 0.67 1.11
2018 2013 678 387,036 0.071 0.051 17,912 17,233 0.96 0.96 1.53
2019 2014 5,345 340,590 0.062 0.062 15,563 10,218 0.66 0.66 1.09
2020 2015 8,237 651,172 0.060 0.062 18,825 10,588 0.56 0.56 0.91
2021 2016 NA 469,230 0.066 0.050 17,091 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2007 16,128.058 21,352 5,224 0.24 0.24 0.31
2013 2008 38,397.443 16,464 21,934 1.33 -1.33 0.52
2014 2009 56,112.745 23,740 32,373 1.36 -1.36 0.52
2015 2010 500.258 31,563 31,062 0.98 0.98 1.55
2016 2011 11,164.587 25,928 14,763 0.57 0.57 0.92
2017 2012 4,050.314 24,461 20,410 0.83 0.83 1.37
2018 2013 678.268 22,045 21,367 0.97 0.97 1.54
2019 2014 5,345.267 14,501 9,156 0.63 0.63 1.04
2020 2015 8,237.087 4,348 3,889 0.89 -0.89 0.44
2021 2016 NA 5,895 NA NA NA NA

Performance summary

Everything is junk here so 5-year avg it is, giving us 6,000.

model range MAD MAPE MPE MAAPE
sibling 5 years 35,520 84.79% 84.79% 1.38
sibling 3 years 36,070 86.24% 86.24% 1.40
ln.sibling 5 years 7,231 54.68% 54.68% 0.85
ln.sibling 3 years 7,369 58.98% 58.98% 0.91
lnY.sibling 5 years 5,816 48.52% 48.52% 0.74
lnY.sibling 3 years 5,557 51.05% 51.05% 0.77
lnS.lnR 5 years 8,350 59.15% 59.15% 0.94
lnS.lnR 3 years 9,444 66.22% 66.22% 1.05
ricker 5 years 10,868 65.42% 65.42% 1.05
ricker 3 years 12,680 72.70% 72.70% 1.18
average 5 years 13,917 77.98% 42.20% 1.06
average 3 years 11,471 83.17% 23.54% 1.01

age.13

Below are model outputs using data from 1972

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 422,833 160,642 0.326 0 540,513 117,679 0.22 0.22 0.27
2013 2008 513,077 52,672 0.328 0 403,565 109,513 0.27 -0.27 0.21
2014 2009 751,758 132,092 0.327 0 505,536 246,222 0.49 -0.49 0.32
2015 2010 1,132,845 567,609 0.320 0 1,040,968 91,877 0.09 -0.09 0.08
2016 2011 1,460,188 507,840 0.351 0 977,593 482,594 0.49 -0.49 0.32
2017 2012 312,468 364,112 0.387 0 825,684 513,216 0.62 0.62 1.02
2018 2013 1,180,877 906,913 0.358 0 1,500,167 319,290 0.21 0.21 0.26
2019 2014 1,115,187 734,904 0.375 0 1,220,280 105,093 0.09 0.09 0.09
2020 2015 652,347 233,249 0.393 0 629,309 23,037 0.04 -0.04 0.04
2021 2016 NA 559,275 0.393 0 1,005,168 NA NA NA NA

ln.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 422,833 160,642 0.400 0 522,171 99,338 0.19 0.19 0.23
2013 2008 513,077 52,672 0.399 0 330,252 182,825 0.55 -0.55 0.34
2014 2009 751,758 132,092 0.390 0 484,681 267,078 0.55 -0.55 0.34
2015 2010 1,132,845 567,609 0.389 0 878,766 254,080 0.29 -0.29 0.22
2016 2011 1,460,188 507,840 0.407 0 854,374 605,813 0.71 -0.71 0.39
2017 2012 312,468 364,112 0.427 0 766,559 454,091 0.59 0.59 0.97
2018 2013 1,180,877 906,913 0.399 0 1,067,053 113,824 0.11 -0.11 0.10
2019 2014 1,115,187 734,904 0.418 0 987,514 127,673 0.13 -0.13 0.11
2020 2015 652,347 233,249 0.432 0 621,623 30,723 0.05 -0.05 0.05
2021 2016 NA 559,275 0.434 0 891,221 NA NA NA NA

lnY.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 422,833 160,642 0.253 0.001 417,578 5,255 0.01 -0.01 0.01
2013 2008 513,077 52,672 0.254 0.001 332,176 180,901 0.54 -0.54 0.34
2014 2009 751,758 132,092 0.247 0.001 399,078 352,680 0.88 -0.88 0.44
2015 2010 1,132,845 567,609 0.237 0.001 990,494 142,351 0.14 -0.14 0.13
2016 2011 1,460,188 507,840 0.263 0.000 888,315 571,873 0.64 -0.64 0.37
2017 2012 312,468 364,112 0.292 0.000 676,653 364,185 0.54 0.54 0.86
2018 2013 1,180,877 906,913 0.274 0.000 2,053,656 872,779 0.42 0.42 0.64
2019 2014 1,115,187 734,904 0.287 0.000 1,289,894 174,707 0.14 0.14 0.16
2020 2015 652,347 233,249 0.305 0.000 491,381 160,966 0.33 -0.33 0.24
2021 2016 NA 559,275 0.304 0.000 914,476 NA NA NA NA

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 422,833 415,452 -0.009 0.408 486,387 63,554 0.13 0.13 0.15
2013 2008 513,077 1,054,704 -0.009 0.407 558,389 45,311 0.08 0.08 0.09
2014 2009 751,758 514,188 -0.007 0.397 497,487 254,271 0.51 -0.51 0.33
2015 2010 1,132,845 518,040 -0.003 0.355 506,449 626,396 1.24 -1.24 0.51
2016 2011 1,460,188 421,380 0.003 0.294 503,652 956,536 1.90 -1.90 0.58
2017 2012 312,468 193,326 0.008 0.258 446,380 133,912 0.30 0.30 0.40
2018 2013 1,180,877 387,036 0.012 0.233 507,804 673,073 1.33 -1.33 0.52
2019 2014 1,115,187 340,590 0.015 0.212 505,338 609,849 1.21 -1.21 0.50
2020 2015 652,347 651,172 0.016 0.204 592,558 59,789 0.10 -0.10 0.09
2021 2016 NA 469,230 0.018 0.186 553,900 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2007 422,833 415,452 0.353 0 619,265 196,432 0.32 0.32 0.43
2013 2008 513,077 1,054,704 0.353 0 486,740 26,337 0.05 -0.05 0.05
2014 2009 751,758 514,188 0.378 0 635,221 116,538 0.18 -0.18 0.15
2015 2010 1,132,845 518,040 0.378 0 638,734 494,111 0.77 -0.77 0.41
2016 2011 1,460,188 421,380 0.371 0 627,963 832,225 1.33 -1.33 0.52
2017 2012 312,468 193,326 0.363 0 441,995 129,527 0.29 0.29 0.39
2018 2013 1,180,877 387,036 0.360 0 621,043 559,834 0.90 -0.90 0.44
2019 2014 1,115,187 340,590 0.357 0 602,454 512,733 0.85 -0.85 0.43
2020 2015 652,347 651,172 0.355 0 673,369 21,022 0.03 0.03 0.03
2021 2016 NA 469,230 0.360 0 669,696 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2007 422,833.2 926,055 503,222 0.54 0.54 0.87
2013 2008 513,077.4 970,159 457,082 0.47 0.47 0.73
2014 2009 751,758.3 818,069 66,311 0.08 0.08 0.09
2015 2010 1,132,845.1 727,959 404,886 0.56 -0.56 0.34
2016 2011 1,460,187.6 720,563 739,624 1.03 -1.03 0.47
2017 2012 312,467.8 856,140 543,673 0.64 0.64 1.05
2018 2013 1,180,877.0 834,067 346,810 0.42 -0.42 0.29
2019 2014 1,115,187.1 967,627 147,560 0.15 -0.15 0.13
2020 2015 652,346.8 1,040,313 387,966 0.37 0.37 0.54
2021 2016 NA 944,213 NA NA NA NA

Performance summary

Sibling models look ok, spawner models do not. Basket of sibling and avg model gives us 939,000.

model range MAD MAPE MPE MAAPE
sibling 5 years 288,646 29.02% 7.81% 0.35
sibling 3 years 149,140 11.19% 8.75% 0.13
ln.sibling 5 years 266,425 31.74% -8.04% 0.32
ln.sibling 3 years 90,740 9.51% -9.51% 0.09
lnY.sibling 5 years 428,902 41.40% 2.55% 0.45
lnY.sibling 3 years 402,817 29.60% 7.76% 0.34
lnS.lnR 5 years 486,632 96.65% -84.65% 0.42
lnS.lnR 3 years 447,570 87.77% -87.77% 0.37
ricker 5 years 411,068 68.04% -55.07% 0.36
ricker 3 years 364,530 59.46% -57.38% 0.30
average 5 years 433,127 52.05% -11.74% 0.49
average 3 years 294,112 31.37% -6.51% 0.32

age.23

Below are model outputs using data from 1972

sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2006 13,218 18,501 0.127 0.022 27,680 14,462 0.52 0.52 0.83
2013 2007 7,949 16,128 0.130 0.019 26,226 18,277 0.70 0.70 1.16
2014 2008 56,710 38,397 0.133 0.016 35,067 21,644 0.62 -0.62 0.36
2015 2009 1,805 56,113 0.134 0.015 43,163 41,358 0.96 0.96 1.53
2016 2010 13,439 500 0.127 0.016 18,838 5,398 0.29 0.29 0.38
2017 2011 3,088 11,165 0.130 0.014 23,070 19,982 0.87 0.87 1.42
2018 2012 0 4,050 0.134 0.012 19,459 19,459 1.00 1.00 1.57
2019 2013 3,254 678 0.139 0.009 17,363 14,109 0.81 0.81 1.34
2020 2014 0 5,345 0.144 0.008 18,892 18,892 1.00 1.00 1.57
2021 2015 NA 8,237 0.149 0.006 19,577 NA NA NA NA

ln.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2006 13,218 18,501 0.287 0.001 21,961 8,743 0.40 0.40 0.58
2013 2007 7,949 16,128 0.283 0.001 20,542 12,592 0.61 0.61 1.01
2014 2008 56,710 38,397 0.274 0.001 27,748 28,962 1.04 -1.04 0.47
2015 2009 1,805 56,113 0.284 0.000 33,069 31,264 0.95 0.95 1.51
2016 2010 13,439 500 0.173 0.005 5,955 7,484 1.26 -1.26 0.51
2017 2011 3,088 11,165 0.161 0.007 17,219 14,131 0.82 0.82 1.36
2018 2012 0 4,050 0.154 0.007 12,112 12,112 1.00 1.00 1.57
2019 2013 3,254 678 0.027 0.154 912 2,343 2.57 -2.57 0.62
2020 2014 0 5,345 0.027 0.152 4,556 4,556 1.00 1.00 1.57
2021 2015 NA 8,237 0.027 0.147 2,801 NA NA NA NA

lnY.sibling

Return Yr Brood Yr Observed Return Sibling Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2006 13,218 18,501 0.135 0.019 17,742 4,524 0.25 0.25 0.33
2013 2007 7,949 16,128 0.138 0.016 17,267 9,318 0.54 0.54 0.86
2014 2008 56,710 38,397 0.142 0.014 19,975 36,735 1.84 -1.84 0.57
2015 2009 1,805 56,113 0.139 0.013 23,547 21,743 0.92 0.92 1.49
2016 2010 13,439 500 0.094 0.034 14,653 1,214 0.08 0.08 0.09
2017 2011 3,088 11,165 0.097 0.030 15,758 12,670 0.80 0.80 1.33
2018 2012 0 4,050 0.102 0.025 14,207 14,207 1.00 1.00 1.57
2019 2013 3,254 678 0.005 0.284 5,064 1,810 0.36 0.36 0.51
2020 2014 0 5,345 0.006 0.271 5,396 5,396 1.00 1.00 1.57
2021 2015 NA 8,237 0.011 0.235 2,380 NA NA NA NA

lnS.lnR

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2006 13,218 305,268 -0.031 0.973 20,162 6,944 0.34 0.34 0.48
2013 2007 7,949 415,452 -0.030 0.966 19,859 11,910 0.60 0.60 0.98
2014 2008 56,710 1,054,704 -0.029 0.901 18,733 37,978 2.03 -2.03 0.59
2015 2009 1,805 514,188 -0.027 0.847 20,465 18,660 0.91 0.91 1.47
2016 2010 13,439 518,040 -0.028 0.924 18,551 5,112 0.28 0.28 0.36
2017 2011 3,088 421,380 -0.027 0.893 18,433 15,345 0.83 0.83 1.37
2018 2012 0 193,326 -0.025 0.803 18,274 18,274 1.00 1.00 1.57
2019 2013 3,254 387,036 -0.022 0.707 14,546 11,292 0.78 0.78 1.29
2020 2014 0 340,590 -0.022 0.736 13,740 13,740 1.00 1.00 1.57
2021 2015 NA 651,172 -0.024 0.862 11,603 NA NA NA NA

ricker

Return Yr Brood Yr Observed Return Spawner Return R Sq P-val Forecasted Return AD APE PE AAPE
2012 2006 13,218 305,268 0.224 0.003 24,544 11,326 0.46 0.46 0.71
2013 2007 7,949 415,452 0.221 0.003 27,010 19,061 0.71 0.71 1.18
2014 2008 56,710 1,054,704 0.218 0.002 21,296 35,415 1.66 -1.66 0.56
2015 2009 1,805 514,188 0.202 0.003 28,355 26,550 0.94 0.94 1.50
2016 2010 13,439 518,040 0.190 0.004 26,152 12,713 0.49 0.49 0.76
2017 2011 3,088 421,380 0.193 0.003 24,639 21,551 0.87 0.87 1.43
2018 2012 0 193,326 0.181 0.004 15,925 15,925 1.00 1.00 1.57
2019 2013 3,254 387,036 0.025 0.163 17,966 14,712 0.82 0.82 1.35
2020 2014 0 340,590 0.025 0.162 16,120 16,120 1.00 1.00 1.57
2021 2015 NA 651,172 0.002 0.308 16,944 NA NA NA NA

average

Return Yr Brood Yr Observed Return Forecasted Return AD APE PE AAPE
2012 2006 13,217.720 25,086 11,868 0.47 0.47 0.73
2013 2007 7,949.202 26,857 18,908 0.70 0.70 1.17
2014 2008 56,710.256 26,085 30,625 1.17 -1.17 0.50
2015 2009 1,804.625 29,642 27,837 0.94 0.94 1.51
2016 2010 13,439.104 26,273 12,834 0.49 0.49 0.76
2017 2011 3,088.118 18,624 15,536 0.83 0.83 1.37
2018 2012 0.000 16,598 16,598 1.00 1.00 1.57
2019 2013 3,254.474 15,008 11,754 0.78 0.78 1.30
2020 2014 0.000 4,317 4,317 1.00 1.00 1.57
2021 2015 NA 3,956 NA NA NA NA

Performance summary

Same story here. Sibling models are ok spawner models are not. Basket of sibling models and running average gives us 10,000.

model range MAD MAPE MPE MAAPE
sibling 5 years 15,568 79.31% 79.31% 1.26
sibling 3 years 17,487 93.75% 93.75% 1.50
ln.sibling 5 years 8,125 132.93% -20.10% 1.13
ln.sibling 3 years 6,337 152.30% -18.97% 1.26
lnY.sibling 5 years 7,059 64.89% 64.89% 1.01
lnY.sibling 3 years 7,138 78.58% 78.58% 1.22
lnS.lnR 5 years 12,752 77.69% 77.69% 1.23
lnS.lnR 3 years 14,435 92.54% 92.54% 1.48
ricker 5 years 16,204 83.59% 83.59% 1.34
ricker 3 years 15,586 93.96% 93.96% 1.50
average 5 years 12,208 82.12% 82.12% 1.32
average 3 years 10,890 92.77% 92.77% 1.48