Early Stopping plot_2

Early Stopping

Here, we present the results of conducting the combined 8 replicates of correlation for within-group 2 prediction (Within), cross-group prediction (Cross), and Early stopping (Early). The purpose was to validate the approach using a pork dataset. Subsequently, a plot was generated, with each color representing a different replicate.

Load the data

• Combined_COR is a dataframe that contains rows representing Within, Cross, and Early-stopping (with 100 stops- Early_1:100) correlation as well as columns representing different replicates.
• The values in input_string objects were obtained from analysis conducted in high-performance computing. Each object represents a different replicate.

Code

input_string <- "
0.2396108 0.2590477 0.2573625 0.2583507 0.2677442 0.2767402 0.2805783
0.2802754 0.2787195 0.2778268 0.2780625 0.2790886 0.2803728 0.2814778
0.2821785 0.2824986 0.2826576 0.2829355 0.2835292 0.2844766 0.2856636
0.2868862 0.2879238 0.2885934 0.2887765 0.2884262 0.2875626 0.2862639
0.2846539 0.2828860 0.2811263 0.2795354 0.2782524 0.2773812 0.2769799
0.2770546 0.2775594 0.2784033 0.2794636 0.2806036 0.2816929 0.2826247
0.2833291 0.2837791 0.2839892 0.2840079 0.2839058 0.2837618 0.2836496
0.2836275 0.2837313 0.2839721 0.2843376 0.2847968 0.2853068 0.2858202
0.2862918 0.2866845 0.2869728 0.2871443 0.2871995 0.2871494 0.2870123
0.2868107 0.2865670 0.2863012 0.2860285 0.2857585 0.2854951 0.2852374
0.2849810 0.2847201 0.2844489 0.2841630 0.2838607 0.2835436 0.2832162
0.2828863 0.2825634 0.2822583 0.2819820 0.2817449 0.2815556 0.2814207
0.2813441 0.2813270 0.2813677 0.2814621 0.2816036 0.2817838 0.2819931
0.2822208 0.2824560 0.2826882 0.2829072 0.2831042 0.2832719 0.2834046 
0.2834986 0.2835523"
num <- scan(text = input_string, what = numeric())

input_string2 <- "
0.4318518 0.4403455 0.4187393 0.3994601 0.3940652 0.3982467 0.4047638
0.4087035 0.4091578 0.4077961 0.4063282 0.4055033 0.4054162 0.4059395
0.4069157 0.4082207 0.4097879 0.4116118 0.4137348 0.4162203 0.4191149
0.4224027 0.4259725 0.4296134 0.4330464 0.4359806 0.4381745 0.4394841
0.4398850 0.4394652 0.4383965 0.4368931 0.4351703 0.4334106 0.4317415
0.4302262 0.4288659 0.4276117 0.4263838 0.4250925 0.4236590 0.4220322
0.4201979 0.4181821 0.4160472 0.4138829 0.4117955 0.4098948 0.4082835
0.4070474 0.4062489 0.4059232 0.4060772 0.4066906 0.4077194 0.4091010
0.4107602 0.4126153 0.4145850 0.4165929 0.4185720 0.4204670 0.4222347
0.4238434 0.4252714 0.4265045 0.4275336 0.4283533 0.4289602 0.4293524
0.4295295 0.4294939 0.4292508 0.4288104 0.4281880 0.4274049 0.4264886
0.4254721 0.4243929 0.4232919 0.4222112 0.4211923 0.4202748 0.4194940
0.4188796 0.4184548 0.4182354 0.4182292 0.4184359 0.4188474 0.4194482
0.4202164 0.4211241 0.4221393 0.4232267 0.4243489 0.4254688 0.4265496
0.4275574 0.4284614"
num2 <- scan(text = input_string2, what = numeric())

input_string3 <- "
0.3344285 0.3430335 0.3319918 0.3229055 0.3285484 0.3415687 0.3531256
0.3609336 0.3662515 0.3704145 0.3741031 0.3775873 0.3808728 0.3837590
0.3859398 0.3871262 0.3871501 0.3860333 0.3840064 0.3814629 0.3788596
0.3765991 0.3749383 0.3739511 0.3735472 0.3735315 0.3736765 0.3737829
0.3737178 0.3734264 0.3729247 0.3722803 0.3715880 0.3709451 0.3704315
0.3700970 0.3699573 0.3699974 0.3701815 0.3704639 0.3708002 0.3711553
0.3715076 0.3718498 0.3721867 0.3725299 0.3728936 0.3732894 0.3737236
0.3741956 0.3746987 0.3752215 0.3757493 0.3762662 0.3767556 0.3772008
0.3775853 0.3778928 0.3781073 0.3782147 0.3782030 0.3780640 0.3777945
0.3773969 0.3768802 0.3762597 0.3755569 0.3747985 0.3740147 0.3732385
0.3725026 0.3718385 0.3712739 0.3708315 0.3705277 0.3703716 0.3703654
0.3705044 0.3707779 0.3711702 0.3716620 0.3722319 0.3728569 0.3735139
0.3741805 0.3748351 0.3754580 0.3760311 0.3765383 0.3769661 0.3773035
0.3775426 0.3776782 0.3777088 0.3776361 0.3774652 0.3772045 0.3768652
0.3768652 0.3768652"
num3 <- scan(text = input_string3, what = numeric())

input_string4 <- "
0.2301838 0.2900746 0.3085393 0.3099474 0.3037447 0.2941311 0.2868531
0.2850660 0.2877788 0.2921569 0.2959077 0.2980332 0.2984915 0.2976617
0.2960115 0.2939518 0.2917901 0.2897449 0.2879979 0.2867372 0.2861550
0.2864041 0.2875451 0.2895162 0.2921373 0.2951435 0.2982336 0.3011239
0.3035932 0.3055129 0.3068550 0.3076796 0.3081052 0.3082723 0.3083088
0.3083044 0.3082992 0.3082853 0.3082206 0.3080483 0.3077175 0.3072000
0.3064996 0.3056532 0.3047247 0.3037934 0.3029406 0.3022369 0.3017330
0.3014540 0.3013991 0.3015442 0.3018485 0.3022614 0.3027303 0.3032072
0.3036534 0.3040424 0.3043607 0.3046064 0.3047869 0.3049153 0.3050073
0.3050777 0.3051381 0.3051951 0.3052501 0.3052988 0.3053328 0.3053405
0.3053087 0.3052243 0.3050753 0.3048522 0.3045487 0.3041622 0.3036940
0.3031496 0.3025378 0.3018711 0.3011643 0.3004344 0.2996997 0.2989787
0.2982898 0.2976502 0.2970756 0.2965794 0.2961727 0.2958637 0.2956580
0.2955588 0.2955663 0.2956789 0.2958928 0.2962023 0.2966002 0.2970779
0.2976254 0.2982317"
num4 <- scan(text = input_string4, what = numeric())

input_string5 <- "
0.3199993 0.2959304 0.2680052 0.2570730 0.2602361 0.2669460 0.2719100
0.2751023 0.2776243 0.2795771 0.2803159 0.2794131 0.2771385 0.2743217
0.2719202 0.2706064 0.2705595 0.2714990 0.2728816 0.2741334 0.2748250
0.2747507 0.2739234 0.2725175 0.2707921 0.2690213 0.2674447 0.2662387
0.2655051 0.2652713 0.2654976 0.2660925 0.2669320 0.2678823 0.2688211
0.2696550 0.2703295 0.2708303 0.2711783 0.2714190 0.2716100 0.2718088
0.2720624 0.2724008 0.2728338 0.2733511 0.2739256 0.2745182 0.2750834
0.2755748 0.2759504 0.2761762 0.2762288 0.2760964 0.2757799 0.2752913
0.2746530 0.2738956 0.2730561 0.2721754 0.2712954 0.2704577 0.2697005
0.2690570 0.2685538 0.2682099 0.2680357 0.2680333 0.2681962 0.2685109
0.2689577 0.2695122 0.2701474 0.2708347 0.2715460 0.2722549 0.2729373
0.2735728 0.2741444 0.2746391 0.2750476 0.2753639 0.2755854 0.2757119
0.2757455 0.2756905 0.2755526 0.2753389 0.2750580 0.2747191 0.2743327
0.2739097 0.2734616 0.2730000 0.2725368 0.2720833 0.2716504 0.2712478
0.2708846 0.2705679"
num5 <- scan(text = input_string5, what = numeric())

input_string6 <- "
0.2841650 0.3023990 0.2887506 0.2952681 0.3120237 0.3208670 0.3191778
0.3128132 0.3074610 0.3057455 0.3074899 0.3109992 0.3144354 0.3167480
0.3178730 0.3183237 0.3186272 0.3190035 0.3193722 0.3195394 0.3193780
0.3189070 0.3182717 0.3176718 0.3172846 0.3172110 0.3174546 0.3179313
0.3184996 0.3189996 0.3192912 0.3192811 0.3189363 0.3182837 0.3173966
0.3163752 0.3153254 0.3143408 0.3134920 0.3128232 0.3123542 0.3120870
0.3120133 0.3121209 0.3123972 0.3128305 0.3134081 0.3141133 0.3149227
0.3158039 0.3167163 0.3176132 0.3184465 0.3191714 0.3197513 0.3201614
0.3203908 0.3204426 0.3203320 0.3200840 0.3197293 0.3193014 0.3188328
0.3183533 0.3178875 0.3174550 0.3170699 0.3167413 0.3164745 0.3162718
0.3161331 0.3160570 0.3160406 0.3160803 0.3161713 0.3163077 0.3164829
0.3166888 0.3169168 0.3171578 0.3174027 0.3176426 0.3178698 0.3180779
0.3182619 0.3184188 0.3185470 0.3186466 0.3187186 0.3187647 0.3187870
0.3187873 0.3187671 0.3187273 0.3186682 0.3185895 0.3184905 0.3183706
0.3182291 0.3180657"
num6 <- scan(text = input_string6, what = numeric())

input_string7 <- "
0.3846014 0.4324586 0.4246500 0.4195546 0.4191923 0.4168005 0.4116155
0.4071129 0.4065327 0.4107214 0.4181594 0.4261751 0.4323564 0.4354344
0.4354254 0.4332304 0.4300446 0.4268717 0.4242948 0.4224900 0.4213768
0.4207875 0.4205842 0.4206996 0.4211196 0.4218372 0.4228119 0.4239525
0.4251266 0.4261891 0.4270147 0.4275228 0.4276886 0.4275393 0.4271398
0.4265745 0.4259281 0.4252728 0.4246605 0.4241223 0.4236721 0.4233126
0.4230419 0.4228576 0.4227586 0.4227449 0.4228155 0.4229662 0.4231877
0.4234655 0.4237806 0.4241115 0.4244368 0.4247374 0.4249982 0.4252086
0.4253628 0.4254586 0.4254972 0.4254815 0.4254159 0.4253053 0.4251552
0.4249708 0.4247577 0.4245216 0.4242689 0.4240064 0.4237419 0.4234838
0.4232414 0.4230241 0.4228414 0.4227019 0.4226128 0.4225796 0.4226051
0.4226895 0.4228301 0.4230215 0.4232559 0.4235237 0.4238140 0.4241154
0.4244167 0.4247072 0.4249777 0.4252205 0.4254297 0.4256014 0.4257334
0.4258254 0.4258786 0.4258955 0.4258796 0.4258351 0.4257669 0.4256797
0.4255785 0.4254678"
num7 <- scan(text = input_string7, what = numeric())

input_string8 <- "
0.3487344 0.3864563 0.3899368 0.3897821 0.3895765 0.3898302 0.3909696
0.3940122 0.3986413 0.4029252 0.4049612 0.4040907 0.4008687 0.3964977
0.3922813 0.3891967 0.3876452 0.3874627 0.3881474 0.3891438 0.3900375
0.3906184 0.3908508 0.3908095 0.3906191 0.3904104 0.3902977 0.3903674
0.3906729 0.3912334 0.3920342 0.3930323 0.3941633 0.3953506 0.3965136
0.3975745 0.3984642 0.3991274 0.3995256 0.3996401 0.3994727 0.3990450
0.3983966 0.3975821 0.3966667 0.3957204 0.3948119 0.3940026 0.3933411
0.3928594 0.3925719 0.3924750 0.3925509 0.3927712 0.3931025 0.3935109
0.3939665 0.3944459 0.3949334 0.3954207 0.3959053 0.3963885 0.3968726
0.3973597 0.3978491 0.3983367 0.3988147 0.3992724 0.3996966 0.4000733
0.4003892 0.4006331 0.4007967 0.4008758 0.4008699 0.4007822 0.4006193
0.4003898 0.4001036 0.3997715 0.3994035 0.3990091 0.3985966 0.3981730
0.3977444 0.3973159 0.3968922 0.3964780 0.3960780 0.3956971 0.3953408
0.3950147 0.3947245 0.3944755 0.3942723 0.3941183 0.3940159 0.3939654
0.3939658 0.3940140"
num8 <- scan(text = input_string8, what = numeric())

#Combine the `num` objects with the within and cross group correlation into a dataframe
Combined_COR <- data.frame(COR.1 = c(0.2834851, 0.332359, num),
                           COR.2 = c(0.4285078, 0.2036959, num2),
                           COR.3 = c(0.3768652, 0.3673465, num3),
                           COR.4 = c(0.3057369, 0.1346875, num4),
                           COR.5 = c(0.2698344, 0.29587, num5),
                           COR.6 = c(0.3176768, 0.1590856, num6),
                           COR.7 = c(0.4250093, 0.2468838, num7),
                           COR.8 = c(0.3958681, 0.3383764, num8)
)
dim(Combined_COR)

[1] 102   8

Code

row.names(Combined_COR)= c("Within", "Cross", paste0("Early_", 1:length(num)))

head(Combined_COR)

            COR.1     COR.2     COR.3     COR.4     COR.5     COR.6     COR.7
Within  0.2834851 0.4285078 0.3768652 0.3057369 0.2698344 0.3176768 0.4250093
Cross   0.3323590 0.2036959 0.3673465 0.1346875 0.2958700 0.1590856 0.2468838
Early_1 0.2396108 0.4318518 0.3344285 0.2301838 0.3199993 0.2841650 0.3846014
Early_2 0.2590477 0.4403455 0.3430335 0.2900746 0.2959304 0.3023990 0.4324586
Early_3 0.2573625 0.4187393 0.3319918 0.3085393 0.2680052 0.2887506 0.4246500
Early_4 0.2583507 0.3994601 0.3229055 0.3099474 0.2570730 0.2952681 0.4195546
            COR.8
Within  0.3958681
Cross   0.3383764
Early_1 0.3487344
Early_2 0.3864563
Early_3 0.3899368
Early_4 0.3897821

Plotting result

Figure 1 Relationship between each parameter (* legend only shows the plot character since each color represents different replicate)

Code

plot(1:100, type = "n", xlim = c(1, 100), ylim = c(0.12, 0.55), xlab = "Index", ylab = "COR") %>%
  {invisible(lapply(seq_len(ncol(Combined_COR)), function(i) points(1:100, Combined_COR[, i][-c(1, 2)], col = i)))}

abline(h=Combined_COR[1,], col=1:8, lty= 2, lwd=1.5)
abline(h=Combined_COR[2,], col=1:8, lty="solid", lwd=1.5)

legend("topright", legend = c("Within","Cross", "Early"), pch= c("¦","|", "o"))

Figure 1: Correlation Plot for Commercial Population