=== Test: test_D_measurement_plus_mlogit ===
Timestamp: 2026-05-11 12:45:12.662143

--- Gradient Check ---
Pass: TRUE
Max error: 1.12e-05

param_idx param_value fixed analytical finite_diff abs_error rel_error pass
1 1 TRUE -142.674499492856 -142.674545288086 4.57952300791931e-05 3.2097687773754e-07 TRUE
2 2 FALSE -16.7119549860307 -16.7119522094727 2.77655800928756e-06 1.66142050580647e-07 TRUE
3 0.5 FALSE 128.101731395634 128.101745605469 1.42098346316288e-05 1.1092615923746e-07 TRUE
4 1.5 FALSE 24.1434250994612 24.1433817545573 4.3344903954079e-05 1.79531204015764e-06 TRUE
5 1.2 FALSE -69.0580329864809 -69.0580495198568 1.65333758985753e-05 2.3941272615615e-07 TRUE
6 0.6 FALSE 60.6354596133227 60.6354827880859 2.31747631929125e-05 3.82198048523924e-07 TRUE
7 1 FALSE -61.6711937310878 -61.6712036132812 9.882193495514e-06 1.60239997219477e-07 TRUE
8 0.8 FALSE -159.448690387837 -159.448638916016 5.14718212230036e-05 3.22811292544897e-07 TRUE
9 0.4 FALSE 212.427313383062 212.427307128906 6.25415572130805e-06 2.94413924736751e-08 TRUE
10 0.5 FALSE -27.0888852766863 -27.0888671875 1.80891862591182e-05 6.67771971928944e-07 TRUE
11 0.6 FALSE -3.36989669905156 -3.36993408203125 3.73829796886938e-05 1.10930892945422e-05 TRUE
12 0.7 FALSE 2.905611215035 2.90557861328125 3.26017537517487e-05 1.12203998207888e-05 TRUE
13 1 FALSE 16.0498231783185 16.0498809814453 5.78031268290147e-05 3.60146763055993e-06 TRUE
14 -0.5 FALSE 6.18416241207913 6.18414306640625 1.93456728823094e-05 3.12827059053658e-06 TRUE
15 0.9 FALSE 9.1555221768743 9.155517578125 4.5987493013655e-06 5.02292662552814e-07 TRUE

--- Hessian Check ---
Pass: TRUE
Max error: 4.97e-05

Summary of relative errors:
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
1.310e-10 3.555e-08 9.547e-08 1.561e-06 5.610e-07 4.968e-05 

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

Parameter estimates:
parameter true_value default_init est_default se_default est_true_init se_true_init z_default z_true_init
f_var 1 1 0.93441808457423 0.0718059263329805 0.934418100333648 0.0718059262838074 -0.913321765694547 -0.913321546847607
T1_int 2 2.01960891905375 2.0169489621474 0.0412123635730513 2.01694895857561 0.0412123632234556 0.411259162978071 0.411259079798814
T1_sigma 0.5 1.06384096857368 0.475224232700912 0.0223425438157904 0.475224222606677 0.0223425430415055 -1.10890539158651 -1.10890588181022
T2_int 1.5 1.55094114192773 1.54778826567428 0.0492737946442172 1.54778826642741 0.0492737938978674 0.969851541155658 0.969851571130597
T2_lambda 1.2 0.5 1.18531102737685 0.0413798859133809 1.18531101687149 0.0413798844837858 -0.354978567459014 -0.354978833598788
T2_sigma 0.6 1.26928237763899 0.581595237601281 0.0258494658146239 0.58159522543257 0.0258494647654253 -0.711997784817155 -0.711998284469195
T3_int 1 1.00263713524346 1.00056520721387 0.0326379533416011 1.00056520595288 0.0326379530778291 0.0173174833592823 0.0173174448634824
T3_lambda 0.8 0.5 0.77893293107127 0.027834940652877 0.778932922547035 0.0278349398416764 -0.756856973091939 -0.756857301391483
T3_sigma 0.4 0.839109411254506 0.392957114859513 0.0176365428274924 0.392957118000944 0.0176365425000492 -0.399334790801973 -0.399334620095528
y1_int 0.5 -0.0378191154681297 0.21108808804939 0.167101411798735 0.211088198692758 0.167101407513698 -1.72896152606173 -1.72896090826499
y1_beta1 0.6 0.721571401567438 0.745320386521823 0.151576213390002 0.745320275242375 0.151576207566698 0.958728175560878 0.958727478245091
y1_loading 0.7 0.5 0.842367480069228 0.171589333244548 0.842367490063749 0.171589329552266 0.829698894314872 0.829698970415197
y2_int 1 0.831972783489226 1.04304120063302 0.145639156519709 1.04304120285539 0.145639156973701 0.295533163343996 0.295533177682153
y2_beta1 -0.5 -0.442889196251955 -0.410417790466011 0.134952625442914 -0.410417773075922 0.134952623643359 0.663804866633612 0.663805004345953
y2_loading 0.9 0.5 1.10163073234547 0.161369205976062 1.10163071350651 0.16136920418346 1.24949943904029 1.24949933617614

Likelihood comparison:
source loglik convergence
True parameters -2080.25288990059 NA
Est (default init) -2071.32267975607 0
Est (true init) -2071.32267975607 0

--- Overall Result ---
Test passed: TRUE
