=== Test: test_D_measurement_plus_mlogit ===
Timestamp: 2026-01-03 16:43:31.011556

--- 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 6.10540190848496e-05 4.27925054409336e-07 TRUE
2 2 FALSE -16.7119549860307 -16.7119598388672 4.85283650419888e-06 2.90381053508313e-07 TRUE
3 0.5 FALSE 128.101731395634 128.101745605469 1.42098346316288e-05 1.1092615923746e-07 TRUE
4 1.5 FALSE 24.1434250994613 24.1433919270833 3.31723779183335e-05 1.37397338445729e-06 TRUE
5 1.2 FALSE -69.0580329864809 -69.0580622355143 2.92490334743434e-05 4.23542632496594e-07 TRUE
6 0.6 FALSE 60.6354596133227 60.6354827880859 2.31747632497559e-05 3.82198049461386e-07 TRUE
7 1 FALSE -61.6711937310878 -61.6712036132812 9.88219344577601e-06 1.60239996412975e-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 2.15129449543383e-05 1.01272038846552e-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 3.73829796860292e-05 1.10930892937515e-05 TRUE
12 0.7 FALSE 2.90561121503501 2.90559387207031 1.73429646981305e-05 5.96881927128141e-06 TRUE
13 1 FALSE 16.0498231783185 16.0498809814453 5.78031268290147e-05 3.60146763055993e-06 TRUE
14 -0.5 FALSE 6.18416241207914 6.18414306640625 1.93456728894148e-05 3.12827059168555e-06 TRUE
15 0.9 FALSE 9.1555221768743 9.155517578125 4.59874929603643e-06 5.02292661970753e-07 TRUE

--- Hessian Check ---
Pass: TRUE
Max error: 4.09e-05

Summary of relative errors:
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
4.100e-10 2.473e-08 8.987e-08 1.872e-06 4.522e-07 4.094e-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 0.934418087980584 0.0718059264698057 0.934418100333648 0.0718059262838074 -0.913321716515883 -0.913321546847604
T1_int 2 2.01960891905375 2.01694896119513 0.0412123636420233 2.01694895857561 0.0412123632234556 0.41125913918328 0.411259079798814
T1_sigma 0.5 1.06384096857368 0.475224231617933 0.0223425437578655 0.475224222606677 0.0223425430415055 -1.10890544293304 -1.10890588181022
T2_int 1.5 1.55094114192773 1.54778826436158 0.0492737946622217 1.54778826642741 0.0492737938978674 0.969851514160377 0.969851571130592
T2_lambda 1.2 0.5 1.1853110247696 0.0413798856729741 1.18531101687149 0.0413798844837858 -0.354978632529032 -0.354978833598788
T2_sigma 0.6 1.26928237763899 0.58159523704462 0.0258494657469126 0.58159522543257 0.0258494647654253 -0.711997808216904 -0.711998284469195
T3_int 1 1.00263713524346 1.00056520633951 0.0326379533638436 1.00056520595288 0.0326379530778291 0.017317456557677 0.0173174448634824
T3_lambda 0.8 0.5 0.778932929135816 0.02783494050017 0.778932922547035 0.0278349398416763 -0.756857046777413 -0.756857301391483
T3_sigma 0.4 0.839109411254507 0.392957115204947 0.0176365428018244 0.392957118000944 0.0176365425000492 -0.399334771796924 -0.399334620095528
y1_int 0.5 -0.0378191154681297 0.211088066051376 0.167101410265886 0.211088198692758 0.167101407513698 -1.72896167356648 -1.72896090826499
y1_beta1 0.6 0.721571401567438 0.745320386076668 0.1515762128821 0.745320275242375 0.151576207566698 0.95872817583655 0.958727478245091
y1_loading 0.7 0.5 0.842367452124327 0.17158933115431 0.842367490063749 0.171589329552266 0.829698741562761 0.829698970415196
y2_int 1 0.831972783489226 1.04304117894604 0.145639154670028 1.04304120285539 0.145639156973701 0.295533018188399 0.295533177682152
y2_beta1 -0.5 -0.442889196251955 -0.410417790590938 0.134952624730826 -0.410417773075922 0.134952623643359 0.66380486921052 0.663805004345953
y2_loading 0.9 0.5 1.10163070141199 0.161369203513514 1.10163071350651 0.16136920418346 1.24949926641428 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
