=== Test: test_H_se_quadratic ===
Timestamp: 2026-01-13 21:29:36.501368

--- Gradient Check ---
Pass: TRUE
Max error: 3.52e-04

param_idx param_value fixed analytical finite_diff abs_error rel_error pass
1 1.5 TRUE -31.2339894298269 -31.2340087890625 1.93592355657302e-05 6.19812707887479e-07 TRUE
2 0.5 FALSE 15.46097518806 15.4609680175781 7.17048186871239e-06 4.63779619785773e-07 TRUE
3 0.8 FALSE -26.7943863301408 -26.794677734375 0.00029140423415086 1.08754520968549e-05 TRUE
4 0.2 FALSE -62.3988066245353 -62.3987426757812 6.39487540325945e-05 1.0248404261103e-06 TRUE
5 0.5 FALSE -9.2122516718133 -9.21261596679688 0.000364294983578262 3.95430554026364e-05 TRUE
6 2 FALSE -18.2354150056945 -18.2354431152344 2.81095399081721e-05 1.54147830302455e-06 TRUE
7 1 FALSE -21.2548239787739 -21.2548828125 5.88337261042682e-05 2.76800990263132e-06 TRUE
8 1.5 FALSE 6.86054359666575 6.8604736328125 6.99638532477564e-05 1.0198108322016e-05 TRUE
9 0.8 FALSE -38.633695047517 -38.6337890625 9.40149830412906e-05 2.43349113101998e-06 TRUE
10 0.9 FALSE 44.1038390366913 44.1036987304688 0.000140306222554898 3.18128017816266e-06 TRUE
11 1 FALSE 2.64029625189206 2.64019775390625 9.84979858120738e-05 3.73070485596555e-05 TRUE
12 1.2 FALSE -18.8675825091681 -18.8675689697266 1.35394415750056e-05 7.17603926437475e-07 TRUE
13 1.1 FALSE -0.649614688699045 -0.649386319247159 0.000228369451885535 0.000351669638113544 TRUE
14 1.8 FALSE 30.3687307326916 30.3687879774306 5.72447389046715e-05 1.88498595818887e-06 TRUE
15 1 FALSE -18.4311417646913 -18.4309692382812 0.000172526410015195 9.36068026508645e-06 TRUE
16 1.2 FALSE -0.201124367330248 -0.201187133789062 6.27664588144228e-05 0.000311980481218203 TRUE
17 0.7 FALSE -52.7582065187069 -52.7581481933594 5.83253474815137e-05 1.10552302305514e-06 TRUE
18 0.8 FALSE 77.6165425629792 77.6163940429688 0.000148520010426978 1.91351340471649e-06 TRUE
19 0.5 FALSE -13.4245168068186 -13.4243774414062 0.000139365412378467 1.03815177267444e-05 TRUE
20 1.1 FALSE 21.5509532157189 21.5507368607955 0.000216354923402662 1.00393283440925e-05 TRUE
21 0.95 FALSE 21.6723163099978 21.6721496582031 0.000166651794692996 7.689675335456e-06 TRUE

--- Hessian Check ---
Pass: TRUE
Max error: 1.02e-05

Summary of relative errors:
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
3.900e-11 1.202e-08 3.726e-08 3.178e-07 1.347e-07 1.021e-05 

--- Estimation Comparison ---
Default init converged: FALSE
True init converged: FALSE
Default estimates reasonable: FALSE
True init estimates reasonable: FALSE

Parameter estimates:
parameter true_value default_init est_default se_default est_true_init se_true_init z_default z_true_init
f1_var 1.5 1 1.67265270771315 0.163679505723087 1.67265284334422 0.163680275143661 1.05482178083578 1.05481765101313
se_intercept 0.5 0 6.4181661687556 0 -4.40821609630908 0 Inf -Inf
se_linear_1 0.8 0.5 0.731579865117149 0.0490303105778523 0.731576879888712 0.0490327765674115 -1.39546607142557 -1.39545677200674
se_quadratic_1 0.2 0 0.161127561281521 0.0249568870351952 0.161126959679117 0.0249573574045195 -1.55758363066914 -1.55757838022722
se_residual_var 0.5 1 0.415218937534749 0.0601300686929223 0.415216280889559 0.0601334849653969 -1.40996117763009 -1.40992525477658
Y1_1_int 2 1.92605997946718 1.94107358657994 0.0721038255285354 1.94107367199677 0.0721039584624761 -0.817243925521517 -0.817241234181298
Y1_1_sigma 1 1.60017510019391 0.939874824817678 0.0428614830984552 0.939874925871904 0.0428615090578538 -1.4027786916335 -1.40277548433819
Y1_2_int 1.5 1.48113872820945 1.49196933159276 0.0601150711902955 1.49196939337236 0.0601151546556096 -0.133588270765181 -0.133587057600544
Y1_2_lambda 0.8 0.5 0.721385827088965 0.0451651357400014 0.72138583769373 0.0451652505199922 -1.74059419113865 -1.74058953290808
Y1_2_sigma 0.9 1.33700907953323 0.955967918058924 0.0360786392783994 0.955967956325344 0.0360786406900169 1.55127574593514 1.55127674587892
Y1_3_int 1 0.961426488303864 0.978953801837112 0.0828417299080467 0.978953903461133 0.082841898801173 -0.254053098435404 -0.254051353764586
Y1_3_lambda 1.2 0.5 1.16742854727739 0.0622962042843018 1.16742867349091 0.0622964300142122 -0.52284811084096 -0.522844190295613
Y1_3_sigma 1.1 1.8376408636098 1.0446613814069 0.0508312073736287 1.04466126934928 0.0508312207974865 -1.08867409318737 -1.0886760101865
Y2_1_int 1.8 2.66202437202684 -4.01461172172376 0 6.81177159661145 0 -Inf Inf
Y2_1_sigma 1 1.55449194834992 0.967621598291364 0.0396973919426879 0.967623274491897 0.0396976771697398 -0.815630451375277 -0.815582366939668
Y2_2_int 1.2 1.76064339820284 -2.69840521429866 0 4.53210172364198 0 -Inf Inf
Y2_2_lambda 0.7 0.5 0.667857526153045 0.0325024059960615 0.667861256851979 0.0325932074615676 -0.988925984459435 -0.986056471610457
Y2_2_sigma 0.8 1.19616040073885 0.877431167896321 0.0321623241221481 0.877430804334802 0.0321639703979832 2.40751158412085 2.40737705503104
Y2_3_int 0.5 1.3571843487813 -6.65424341165522 0 6.33657664124381 0 -Inf Inf
Y2_3_lambda 1.1 0.5 1.19991767506624 0.0174379653035691 1.19992520901511 0.0172500896820591 5.72989298503694 5.7927356238056
Y2_3_sigma 0.95 1.7480532860858 0.961963699489152 0.0481591725046744 0.961961695664632 0.0481487900899635 0.24841995547142 0.248431905397456

Likelihood comparison:
source loglik convergence
True parameters -4847.26777097663 NA
Est (default init) -4835.13873584794 1
Est (true init) -4835.13873579691 1

--- Overall Result ---
Test passed: FALSE
