=== Test: test_D_measurement_plus_mlogit ===
Timestamp: 2025-12-04 11:48:48.221887

--- Gradient Check ---
Pass: TRUE
Max error: 1.11e-05

param_idx param_value fixed analytical finite_diff abs_error rel_error pass
1 1 TRUE -142.674499492856 -142.674560546875 6.10540190564279e-05 4.2792505421013e-07 TRUE
2 2 FALSE -16.7119549860307 -16.7119598388672 4.85283650064616e-06 2.90381053295728e-07 TRUE
3 0.5 FALSE 128.101731395634 128.101745605469 1.42098346600505e-05 1.10926159459328e-07 TRUE
4 1.5 FALSE 24.1434250994612 24.1433919270833 3.31723779076754e-05 1.37397338401584e-06 TRUE
5 1.2 FALSE -69.0580329864808 -69.0580622355143 2.92490334885542e-05 4.23542632702376e-07 TRUE
6 0.6 FALSE 60.6354596133227 60.6354827880859 2.31747632426504e-05 3.82198049344203e-07 TRUE
7 1 FALSE -61.6711937310878 -61.6712036132812 9.8821934173543e-06 1.60239995952116e-07 TRUE
8 0.8 FALSE -159.448690387837 -159.448654174805 3.62130322457688e-05 2.27114066488565e-07 TRUE
9 0.4 FALSE 212.427313383062 212.427291870117 2.15129450396034e-05 1.01272039247937e-07 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 2.90561121503501 2.90559387207031 1.73429646981305e-05 5.96881927128141e-06 TRUE
13 1 FALSE 16.0498231783185 16.0498809814453 5.78031268148038e-05 3.60146762967451e-06 TRUE
14 -0.5 FALSE 6.18416241207914 6.18414306640625 1.93456728876384e-05 3.12827059139831e-06 TRUE
15 0.9 FALSE 9.1555221768743 9.155517578125 4.59874929781279e-06 5.02292662164774e-07 TRUE

--- Hessian Check ---
Pass: TRUE
Max error: 5.36e-05

Summary of relative errors:
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
0.000e+00 2.000e-08 8.000e-08 5.312e-04 4.700e-07 6.351e-02 

--- 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 0.934417723877668 0.0752724248010363 0.93441741475337 0.0752724077754017 -0.871265623442875 -0.871269927252963
T1_int 2 2.01960891905375 2.01694901905077 0.0413660165160974 2.01694906782034 0.0413660153957168 0.409732927611498 0.409734117685811
T1_sigma 0.5 1.06384096857368 0.4752242483196 0.0223639336769017 0.475224261701896 0.0223639345155955 -1.10784408674889 -1.10784344681507
T2_int 1.5 1.55094114192773 1.5477883328814 0.0494530779349961 1.54778839048091 0.0494530785509619 0.966336876831238 0.966338029525615
T2_lambda 1.2 0.5 1.1853111177719 0.0417650473968332 1.18531119523835 0.0417650533242987 -0.351702754902489 -0.351700850172424
T2_sigma 0.6 1.26928237763899 0.581595231698495 0.0258521098139909 0.581595226640801 0.0258521118437507 -0.711925194265762 -0.711925334008944
T3_int 1 1.00263713524346 1.00056525137332 0.0327548123961706 1.00056528921992 0.0327548127575927 0.0172570481089556 0.017258203370211
T3_lambda 0.8 0.5 0.778932992738646 0.0281013820877871 0.778933045586542 0.0281013856119366 -0.749678688241814 -0.749676713610506
T3_sigma 0.4 0.839109411254507 0.392957107031549 0.0176433504710075 0.392957100322964 0.0176433512593299 -0.399181152130037 -0.399181514527299
y1_int 0.5 -0.0378191154681297 0.211088134838519 0.16712707762179 0.211088174940151 0.167127079083186 -1.72869572826069 -1.72869547319764
y1_beta1 0.6 0.721571401567438 0.745320387059582 0.15157621707747 0.745320387520354 0.151576217034973 0.958728155785209 0.958728159093876
y1_loading 0.7 0.5 0.842367527466281 0.171614993370107 0.842367568087615 0.171615004338957 0.829575112701545 0.82957529637924
y2_int 1 0.831972783489226 1.04304125935104 0.145685531052834 1.04304130967587 0.14568553263679 0.295439492446439 0.29543983466896
y2_beta1 -0.5 -0.442889196251955 -0.410417784833288 0.134953086118342 -0.41041778000625 0.134953086118204 0.663802642409794 0.663802678178738
y2_loading 0.9 0.5 1.10163081678849 0.161455771587759 1.10163088915867 0.161455782389236 1.24883003441531 1.24883039910319

Likelihood comparison:
source loglik convergence
True parameters -2080.25288990059 NA
Est (default init) -2071.32267975608 0
Est (true init) -2071.32267975612 0

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