This function will be called after an instance is built. User
input will be stored in the environment. The response variable of this model
is y. The formula of y is defined in POLY_MODEL$formula, the null
formula is defined in POLY_MODEL$null_formula, the alternative is
defined in POLY_MODEL$alt_formula. The formula for the raw
orthogonal polynomial term is defined in POLY_MODEL$raw_z_formula, and
the scaled orthogonal polynomial term is defined in POLY_MODEL$z_formula.
Arguments
- shape
Integer. The shape of the orthogonal polynomial used in the model. Note it should be a value between 1 to 4. Default is
shape = 1.- sigma
Positive numeric. Default is
sigma = 1.- include_z
Boolean. Whether or not to include
zin the formula ofy. Default isinclude_z = TRUE.- x
Random variable or closed form expression. Default is
x = rand_uniform(-1, 1, env = new.env(parent = parent.env(self))).- e
Random variable or closed form expression. Default is
e = rand_normal(0, sigma, env = new.env(parent = parent.env(self))).
Examples
# Instantiate
x <- rand_uniform()
e <- rand_normal(sigma = 0.5)
test <- poly_model(shape = 1, x = x, e = e)
test
#>
#> ── <POLY_MODEL object>
#> y = 1 + x + include_z * z + e
#> - x: <RAND_UNIFORM object>
#> [a: 0, b: 1]
#> - z: <CLOSED_FORM object>
#> EXPR = (raw_z - min(raw_z))/max(raw_z - min(raw_z)) * 2 - 1
#> - raw_z: <CLOSED_FORM object>
#> EXPR = hermite(shape)((x - min(x))/max(x - min(x)) * 4 - 2)
#> - x: <RAND_UNIFORM object>
#> [a: 0, b: 1]
#> - e: <RAND_NORMAL object>
#> [mu: 0, sigma: 0.5]
#> Parameters:
#> - shape: 1
#> - include_z: TRUE
#> - sigma: 1
# Generate data
test$gen(10)
#> y x raw_z z e .resid
#> 1 2.82918402 0.99206147 3.0000000 1.0000000 -0.16287746 0.43127384
#> 2 1.18415371 0.32417575 -0.4060480 -0.7046933 0.56467131 0.14006221
#> 3 1.45230931 0.23659775 0.2859441 -0.3583581 0.57406970 0.58574029
#> 4 1.10669575 0.64739654 -0.6748962 -0.8392492 0.29854844 -0.59257122
#> 5 0.12738603 0.40899947 -0.8246092 -0.9141791 -0.36743434 -1.08864498
#> 6 0.91455446 0.52503913 -0.9960829 -1.0000000 0.38951532 -0.53669143
#> 7 3.24321498 0.92981657 2.0338006 0.5164267 0.79697167 0.97147655
#> 8 1.57651064 0.02784324 3.0000000 1.0000000 -0.45133259 1.13309149
#> 9 0.05887894 0.40170245 -0.7983379 -0.9010306 -0.44179295 -1.14236085
#> 10 0.95571796 0.23192334 0.3302999 -0.3361585 0.05995314 0.09862408
#> .fitted
#> 1 2.3979102
#> 2 1.0440915
#> 3 0.8665690
#> 4 1.6992670
#> 5 1.2160310
#> 6 1.4512459
#> 7 2.2717384
#> 8 0.4434191
#> 9 1.2012398
#> 10 0.8570939
# Generate lineup
test$gen_lineup(10, k = 3)
#> y x raw_z z e .resid
#> 1 0.5661146 0.464207984 -0.8315598 -0.9158039 0.01771045 -0.72833381
#> 2 -0.6533803 0.386998348 -0.9999500 -1.0000000 -1.04037869 -1.84380747
#> 3 1.5131674 0.002796276 3.0000000 1.0000000 -0.48962883 0.84035936
#> 4 2.1179047 0.768493104 3.0000000 1.0000000 -0.65058840 0.41350599
#> 5 0.7062670 0.431980628 -0.9414075 -0.9707284 0.24501472 -0.54476286
#> 6 3.1096976 0.724419444 2.1320477 0.5660184 0.81925975 1.46467745
#> 7 0.6738162 0.536686856 -0.3774092 -0.6887257 -0.17414497 -0.71827989
#> 8 0.2255530 0.494252309 -0.6780956 -0.8390708 -0.42962847 -1.10937278
#> 9 2.7763821 0.680455114 1.3718759 0.1859278 0.90999921 1.19059319
#> 10 1.7428003 0.028456856 2.4817662 0.7408799 -0.02653640 1.03542082
#> 11 1.3539328 0.464207984 -0.8315598 -0.9158039 0.01771045 0.05948446
#> 12 0.2050582 0.386998348 -0.9999500 -1.0000000 -1.04037869 -0.98536897
#> 13 -0.1714869 0.002796276 3.0000000 1.0000000 -0.48962883 -0.84429503
#> 14 2.2200728 0.768493104 3.0000000 1.0000000 -0.65058840 0.51567408
#> 15 3.3877251 0.431980628 -0.9414075 -0.9707284 0.24501472 2.13669531
#> 16 0.8792281 0.724419444 2.1320477 0.5660184 0.81925975 -0.76579210
#> 17 2.8587838 0.536686856 -0.3774092 -0.6887257 -0.17414497 1.46668776
#> 18 0.5664912 0.494252309 -0.6780956 -0.8390708 -0.42962847 -0.76843462
#> 19 0.3700902 0.680455114 1.3718759 0.1859278 0.90999921 -1.21569872
#> 20 1.1084273 0.028456856 2.4817662 0.7408799 -0.02653640 0.40104782
#> 21 2.5209435 0.464207984 -0.8315598 -0.9158039 0.01771045 1.22649515
#> 22 -0.2402070 0.386998348 -0.9999500 -1.0000000 -1.04037869 -1.43063414
#> 23 1.2726077 0.002796276 3.0000000 1.0000000 -0.48962883 0.59979959
#> 24 0.4758463 0.768493104 3.0000000 1.0000000 -0.65058840 -1.22855243
#> 25 3.0939044 0.431980628 -0.9414075 -0.9707284 0.24501472 1.84287453
#> 26 2.2088480 0.724419444 2.1320477 0.5660184 0.81925975 0.56382785
#> 27 0.5499036 0.536686856 -0.3774092 -0.6887257 -0.17414497 -0.84219246
#> 28 0.7270716 0.494252309 -0.6780956 -0.8390708 -0.42962847 -0.60785420
#> 29 2.3191896 0.680455114 1.3718759 0.1859278 0.90999921 0.73340076
#> 30 -0.1497851 0.028456856 2.4817662 0.7408799 -0.02653640 -0.85716465
#> .fitted test_name statistic p_value k null
#> 1 1.2944484 F-test 20.1814245 0.002824028 3 FALSE
#> 2 1.1904271 F-test 20.1814245 0.002824028 3 FALSE
#> 3 0.6728081 F-test 20.1814245 0.002824028 3 FALSE
#> 4 1.7043987 F-test 20.1814245 0.002824028 3 FALSE
#> 5 1.2510298 F-test 20.1814245 0.002824028 3 FALSE
#> 6 1.6450202 F-test 20.1814245 0.002824028 3 FALSE
#> 7 1.3920961 F-test 20.1814245 0.002824028 3 FALSE
#> 8 1.3349258 F-test 20.1814245 0.002824028 3 FALSE
#> 9 1.5857889 F-test 20.1814245 0.002824028 3 FALSE
#> 10 0.7073795 F-test 20.1814245 0.002824028 3 FALSE
#> 11 1.2944484 F-test 0.4726027 0.513917579 1 TRUE
#> 12 1.1904271 F-test 0.4726027 0.513917579 1 TRUE
#> 13 0.6728081 F-test 0.4726027 0.513917579 1 TRUE
#> 14 1.7043987 F-test 0.4726027 0.513917579 1 TRUE
#> 15 1.2510298 F-test 0.4726027 0.513917579 1 TRUE
#> 16 1.6450202 F-test 0.4726027 0.513917579 1 TRUE
#> 17 1.3920961 F-test 0.4726027 0.513917579 1 TRUE
#> 18 1.3349258 F-test 0.4726027 0.513917579 1 TRUE
#> 19 1.5857889 F-test 0.4726027 0.513917579 1 TRUE
#> 20 0.7073795 F-test 0.4726027 0.513917579 1 TRUE
#> 21 1.2944484 F-test 0.1342374 0.724901776 2 TRUE
#> 22 1.1904271 F-test 0.1342374 0.724901776 2 TRUE
#> 23 0.6728081 F-test 0.1342374 0.724901776 2 TRUE
#> 24 1.7043987 F-test 0.1342374 0.724901776 2 TRUE
#> 25 1.2510298 F-test 0.1342374 0.724901776 2 TRUE
#> 26 1.6450202 F-test 0.1342374 0.724901776 2 TRUE
#> 27 1.3920961 F-test 0.1342374 0.724901776 2 TRUE
#> 28 1.3349258 F-test 0.1342374 0.724901776 2 TRUE
#> 29 1.5857889 F-test 0.1342374 0.724901776 2 TRUE
#> 30 0.7073795 F-test 0.1342374 0.724901776 2 TRUE
# Plot the lineup
test$plot_lineup(test$gen_lineup(100))
test <- poly_model(shape = 1, include_z = FALSE, x = x, e = e)
test$plot_lineup(test$gen_lineup(100))
test <- poly_model(shape = 2, x = x, e = e)
test$plot_lineup(test$gen_lineup(100))
test <- poly_model(shape = 3, x = x, e = e)
test$plot_lineup(test$gen_lineup(100))
test <- poly_model(shape = 4, x = x, e = e)
test$plot_lineup(test$gen_lineup(100))
