With Starting Values
Ivan Jacob Agaloos Pesigan
Source:vignettes/sim-all-starts.Rmd
sim-all-starts.RmdWe generate data using the CULTA model with two latent profiles, where profile membership depends on a covariate and profile transitions follow a multinomial structure. However, for model fitting, we impose a simpler structure by fitting a CUTS (1 Profile) model with autoregressive effects, ignoring the latent profiles during estimation. We then compare this misspecified model to the correctly specified two-profile CULTA model.
Data Generation
# complete list of R function arguments
# random seed for reproducibility
set.seed(42)
# dimensions
n # number of individuals
#> [1] 200
m # measurement occasions
#> [1] 6
p # number of items
#> [1] 4
q # common trait dimension
#> [1] 1
# covariate parameters
mu_x
#> [1] 0
sigma_x
#> [1] 1
# profile membership and transition parameters
nu_0
#> [1] -0.405
kappa_0
#> [1] 0.1
alpha_0
#> [1] -0.5
beta_00
#> [1] 0.85
gamma_00
#> [1] 0.2
gamma_10
#> [1] 0.2
# trait parameters
psi_t
#> [,1]
#> [1,] 0.3
mu_t
#> [1] 0
psi_p
#> [,1] [,2] [,3] [,4]
#> [1,] 0.3 0.0 0.0 0.0
#> [2,] 0.0 0.3 0.0 0.0
#> [3,] 0.0 0.0 0.3 0.0
#> [4,] 0.0 0.0 0.0 0.3
mu_p
#> [1] 0 0 0 0
common_trait_loading
#> [,1]
#> [1,] 1
#> [2,] 1
#> [3,] 1
#> [4,] 1
# state parameters
common_state_loading
#> [,1]
#> [1,] 1
#> [2,] 1
#> [3,] 1
#> [4,] 1
phi_0
#> [1] 0
phi_1
#> [1] 0.311
psi_s0
#> [1] 1
psi_s
#> [1] 0.5
theta
#> [,1] [,2] [,3] [,4]
#> [1,] 0.2 0.0 0.0 0.0
#> [2,] 0.0 0.2 0.0 0.0
#> [3,] 0.0 0.0 0.2 0.0
#> [4,] 0.0 0.0 0.0 0.2
# profile-specific means
mu_profile
#> [,1] [,2]
#> [1,] 2.253 -0.278
#> [2,] 1.493 -0.165
#> [3,] 1.574 -0.199
#> [4,] 1.117 -0.148
# starting values
starting_values
#> $nu_0
#> [1] -0.405
#>
#> $kappa_0
#> [1] 0.1
#>
#> $alpha_0
#> [1] -0.5
#>
#> $beta_00
#> [1] 0.85
#>
#> $gamma_00
#> [1] 0.2
#>
#> $gamma_10
#> [1] 0.2
#>
#> $psi_t
#> [,1]
#> [1,] 0.3
#>
#> $psi_p
#> [,1] [,2] [,3] [,4]
#> [1,] 0.3 0.0 0.0 0.0
#> [2,] 0.0 0.3 0.0 0.0
#> [3,] 0.0 0.0 0.3 0.0
#> [4,] 0.0 0.0 0.0 0.3
#>
#> $common_trait_loading
#> [,1]
#> [1,] 1
#> [2,] 1
#> [3,] 1
#> [4,] 1
#>
#> $common_state_loading
#> [,1]
#> [1,] 1
#> [2,] 1
#> [3,] 1
#> [4,] 1
#>
#> $phi_0
#> [1] 0
#>
#> $phi_1
#> [1] 0.311
#>
#> $psi_s0
#> [1] 1
#>
#> $psi_s
#> [1] 0.5
#>
#> $theta
#> [,1] [,2] [,3] [,4]
#> [1,] 0.2 0.0 0.0 0.0
#> [2,] 0.0 0.2 0.0 0.0
#> [3,] 0.0 0.0 0.2 0.0
#> [4,] 0.0 0.0 0.0 0.2
#>
#> $mu_profile
#> [,1] [,2]
#> [1,] 2.253 -0.278
#> [2,] 1.493 -0.165
#> [3,] 1.574 -0.199
#> [4,] 1.117 -0.148
data <- GenCULTA2Profiles(
n = n,
m = m,
mu_x = mu_x,
sigma_x = sigma_x,
nu_0 = nu_0,
kappa_0 = kappa_0,
alpha_0 = alpha_0,
beta_00 = beta_00,
gamma_00 = gamma_00,
gamma_10 = gamma_10,
mu_t = mu_t,
psi_t = psi_t,
mu_p = mu_p,
psi_p = psi_p,
common_trait_loading = common_trait_loading,
common_state_loading = common_state_loading,
phi_0 = phi_0,
phi_1 = phi_1,
psi_s0 = psi_s0,
psi_s = psi_s,
theta = theta,
mu_profile = mu_profile
)Model Fitting
The FitCULTA1Profiles function fits the misspecified
one-profile model using Mplus. Note: This
function requires that Mplus is already installed on
the system.
one_profile_starts <- FitCULTA1Profile(
data = data,
starts = 1000,
starting_values = starting_values
)
summary(one_profile_starts)
#> est se z p 2.5% 97.5%
#> mu_1 0.8760 0.0756 11.5939 0.0000 0.7279 1.0241
#> mu_2 0.6893 0.0680 10.1375 0.0000 0.5561 0.8226
#> mu_3 0.6653 0.0693 9.5992 0.0000 0.5295 0.8011
#> mu_4 0.5206 0.0616 8.4480 0.0000 0.3999 0.6414
#> lambda_t2 0.9405 0.1094 8.5960 0.0000 0.7260 1.1549
#> lambda_s2 0.7756 0.0146 53.0696 0.0000 0.7470 0.8043
#> lambda_t3 0.9325 0.1525 6.1157 0.0000 0.6337 1.2314
#> lambda_s3 0.8070 0.0145 55.5545 0.0000 0.7785 0.8355
#> lambda_t4 0.7139 0.1305 5.4708 0.0000 0.4582 0.9697
#> lambda_s4 0.6782 0.0137 49.4419 0.0000 0.6513 0.7051
#> theta_11 0.2968 0.0198 14.9955 0.0000 0.2580 0.3356
#> theta_22 0.2219 0.0125 17.6984 0.0000 0.1973 0.2465
#> theta_33 0.1966 0.0126 15.6618 0.0000 0.1720 0.2212
#> theta_44 0.2273 0.0112 20.3052 0.0000 0.2054 0.2493
#> phi 0.2302 0.0430 5.3475 0.0000 0.1458 0.3145
#> psi_t 0.3828 0.1265 3.0269 0.0025 0.1349 0.6306
#> psi_p_11 0.2208 0.0479 4.6083 0.0000 0.1269 0.3147
#> psi_p_22 0.2495 0.0383 6.5065 0.0000 0.1743 0.3246
#> psi_p_33 0.2732 0.0501 5.4483 0.0000 0.1749 0.3714
#> psi_p_44 0.3006 0.0451 6.6618 0.0000 0.2122 0.3891
#> psi_s0 2.9677 0.2988 9.9310 0.0000 2.3820 3.5534
#> psi_s 1.8330 0.0883 20.7648 0.0000 1.6600 2.0060
one_profile <- FitCULTA1Profile(
data = data,
starts = 1000
)
summary(one_profile)
#> est se z p 2.5% 97.5%
#> mu_1 0.8760 0.0756 11.5939 0.0000 0.7279 1.0241
#> mu_2 0.6893 0.0680 10.1375 0.0000 0.5561 0.8226
#> mu_3 0.6653 0.0693 9.5992 0.0000 0.5295 0.8011
#> mu_4 0.5206 0.0616 8.4480 0.0000 0.3999 0.6414
#> lambda_t2 0.9405 0.1094 8.5960 0.0000 0.7260 1.1549
#> lambda_s2 0.7756 0.0146 53.0696 0.0000 0.7470 0.8043
#> lambda_t3 0.9325 0.1525 6.1158 0.0000 0.6337 1.2314
#> lambda_s3 0.8070 0.0145 55.5545 0.0000 0.7785 0.8355
#> lambda_t4 0.7139 0.1305 5.4709 0.0000 0.4582 0.9697
#> lambda_s4 0.6782 0.0137 49.4419 0.0000 0.6513 0.7051
#> theta_11 0.2968 0.0198 14.9955 0.0000 0.2580 0.3356
#> theta_22 0.2219 0.0125 17.6984 0.0000 0.1973 0.2465
#> theta_33 0.1966 0.0126 15.6618 0.0000 0.1720 0.2212
#> theta_44 0.2273 0.0112 20.3052 0.0000 0.2054 0.2493
#> phi 0.2302 0.0430 5.3475 0.0000 0.1458 0.3145
#> psi_t 0.3828 0.1265 3.0269 0.0025 0.1349 0.6306
#> psi_p_11 0.2208 0.0479 4.6083 0.0000 0.1269 0.3147
#> psi_p_22 0.2495 0.0383 6.5065 0.0000 0.1743 0.3246
#> psi_p_33 0.2732 0.0501 5.4483 0.0000 0.1749 0.3714
#> psi_p_44 0.3006 0.0451 6.6618 0.0000 0.2122 0.3891
#> psi_s0 2.9677 0.2988 9.9310 0.0000 2.3820 3.5534
#> psi_s 1.8330 0.0883 20.7648 0.0000 1.6600 2.0060
summary(one_profile_starts) - summary(one_profile)
#> est se z p 2.5% 97.5%
#> mu_1 0 0 0e+00 0 0 0
#> mu_2 0 0 0e+00 0 0 0
#> mu_3 0 0 0e+00 0 0 0
#> mu_4 0 0 0e+00 0 0 0
#> lambda_t2 0 0 0e+00 0 0 0
#> lambda_s2 0 0 0e+00 0 0 0
#> lambda_t3 0 0 -1e-04 0 0 0
#> lambda_s3 0 0 0e+00 0 0 0
#> lambda_t4 0 0 -1e-04 0 0 0
#> lambda_s4 0 0 0e+00 0 0 0
#> theta_11 0 0 0e+00 0 0 0
#> theta_22 0 0 0e+00 0 0 0
#> theta_33 0 0 0e+00 0 0 0
#> theta_44 0 0 0e+00 0 0 0
#> phi 0 0 0e+00 0 0 0
#> psi_t 0 0 0e+00 0 0 0
#> psi_p_11 0 0 0e+00 0 0 0
#> psi_p_22 0 0 0e+00 0 0 0
#> psi_p_33 0 0 0e+00 0 0 0
#> psi_p_44 0 0 0e+00 0 0 0
#> psi_s0 0 0 0e+00 0 0 0
#> psi_s 0 0 0e+00 0 0 0The FitLTA2Profiles function fits the misspecified
two-profile LTA model using Mplus.
lta_starts <- FitLTA2Profiles(
data = data,
ncores = parallel::detectCores(),
starts = c(500, 100),
stiterations = 200,
stscale = 2,
starting_values = starting_values
)
summary(lta_starts)
#> est se z p 2.5% 97.5%
#> mu_10 2.1869 0.0983 22.2454 0.0000 1.9943 2.3796
#> mu_20 1.7065 0.0886 19.2540 0.0000 1.5328 1.8802
#> mu_30 1.7080 0.0933 18.3092 0.0000 1.5252 1.8909
#> mu_40 1.4069 0.0718 19.5976 0.0000 1.2662 1.5476
#> theta_11 1.2348 0.0699 17.6596 0.0000 1.0978 1.3718
#> theta_22 1.0071 0.0562 17.9177 0.0000 0.8969 1.1172
#> theta_33 1.0504 0.0658 15.9581 0.0000 0.9214 1.1795
#> theta_44 0.8839 0.0507 17.4488 0.0000 0.7847 0.9832
#> mu_11 -0.4860 0.1050 -4.6287 0.0000 -0.6918 -0.2802
#> mu_21 -0.3674 0.0886 -4.1472 0.0000 -0.5410 -0.1938
#> mu_31 -0.4181 0.0921 -4.5386 0.0000 -0.5986 -0.2375
#> mu_41 -0.4001 0.0833 -4.8030 0.0000 -0.5633 -0.2368
#> nu_0 0.0347 0.1507 0.2300 0.8181 -0.2607 0.3301
#> alpha_0 -0.5490 0.1362 -4.0298 0.0001 -0.8161 -0.2820
#> kappa_0 0.4532 0.1661 2.7285 0.0064 0.1277 0.7788
#> beta_00 1.2141 0.1832 6.6269 0.0000 0.8550 1.5732
#> gamma_00 0.1396 0.1121 1.2456 0.2129 -0.0801 0.3592
#> gamma_10 0.1272 0.1202 1.0582 0.2899 -0.1084 0.3629
lta <- FitLTA2Profiles(
data = data,
ncores = parallel::detectCores(),
starts = c(500, 100),
stiterations = 200,
stscale = 2
)
summary(lta)
#> est se z p 2.5% 97.5%
#> mu_10 2.1870 0.0983 22.2453 0.0000 1.9943 2.3796
#> mu_20 1.7065 0.0886 19.2539 0.0000 1.5328 1.8802
#> mu_30 1.7080 0.0933 18.3091 0.0000 1.5252 1.8909
#> mu_40 1.4069 0.0718 19.5975 0.0000 1.2662 1.5476
#> theta_11 1.2348 0.0699 17.6596 0.0000 1.0977 1.3718
#> theta_22 1.0071 0.0562 17.9177 0.0000 0.8969 1.1172
#> theta_33 1.0504 0.0658 15.9581 0.0000 0.9214 1.1795
#> theta_44 0.8840 0.0507 17.4488 0.0000 0.7847 0.9832
#> mu_11 -0.4860 0.1050 -4.6285 0.0000 -0.6917 -0.2802
#> mu_21 -0.3674 0.0886 -4.1471 0.0000 -0.5410 -0.1938
#> mu_31 -0.4180 0.0921 -4.5385 0.0000 -0.5986 -0.2375
#> mu_41 -0.4001 0.0833 -4.8028 0.0000 -0.5633 -0.2368
#> nu_0 0.0346 0.1507 0.2299 0.8182 -0.2608 0.3300
#> alpha_0 -0.5490 0.1362 -4.0299 0.0001 -0.8161 -0.2820
#> kappa_0 0.4532 0.1661 2.7285 0.0064 0.1277 0.7788
#> beta_00 1.2141 0.1832 6.6268 0.0000 0.8550 1.5732
#> gamma_00 0.1396 0.1121 1.2455 0.2129 -0.0801 0.3592
#> gamma_10 0.1273 0.1202 1.0584 0.2899 -0.1084 0.3629
summary(lta_starts) - summary(lta)
#> est se z p 2.5% 97.5%
#> mu_10 -1e-04 0 1e-04 0e+00 0e+00 0e+00
#> mu_20 0e+00 0 1e-04 0e+00 0e+00 0e+00
#> mu_30 0e+00 0 1e-04 0e+00 0e+00 0e+00
#> mu_40 0e+00 0 1e-04 0e+00 0e+00 0e+00
#> theta_11 0e+00 0 0e+00 0e+00 1e-04 0e+00
#> theta_22 0e+00 0 0e+00 0e+00 0e+00 0e+00
#> theta_33 0e+00 0 0e+00 0e+00 0e+00 0e+00
#> theta_44 -1e-04 0 0e+00 0e+00 0e+00 0e+00
#> mu_11 0e+00 0 -2e-04 0e+00 -1e-04 0e+00
#> mu_21 0e+00 0 -1e-04 0e+00 0e+00 0e+00
#> mu_31 -1e-04 0 -1e-04 0e+00 0e+00 0e+00
#> mu_41 0e+00 0 -2e-04 0e+00 0e+00 0e+00
#> nu_0 1e-04 0 1e-04 -1e-04 1e-04 1e-04
#> alpha_0 0e+00 0 1e-04 0e+00 0e+00 0e+00
#> kappa_0 0e+00 0 0e+00 0e+00 0e+00 0e+00
#> beta_00 0e+00 0 1e-04 0e+00 0e+00 0e+00
#> gamma_00 0e+00 0 1e-04 0e+00 0e+00 0e+00
#> gamma_10 -1e-04 0 -2e-04 0e+00 0e+00 0e+00The FitRILTA2Profiles function fits the misspecified
two-profile RILTA model using Mplus.
rilta_starts <- FitRILTA2Profiles(
data = data,
ncores = parallel::detectCores(),
starts = c(500, 100),
stiterations = 200,
stscale = 2,
starting_values = starting_values
)
summary(rilta_starts)
#> est se z p 2.5% 97.5%
#> mu_10 2.2036 0.0838 26.2943 0.0000 2.0393 2.3678
#> mu_20 1.6653 0.0791 21.0455 0.0000 1.5102 1.8204
#> mu_30 1.6534 0.0807 20.5009 0.0000 1.4953 1.8115
#> mu_40 1.3753 0.0703 19.5698 0.0000 1.2375 1.5130
#> lambda_t1 0.8898 0.0775 11.4746 0.0000 0.7378 1.0418
#> lambda_t2 0.8338 0.0696 11.9803 0.0000 0.6974 0.9702
#> lambda_t3 0.8936 0.0698 12.7993 0.0000 0.7567 1.0304
#> lambda_t4 0.6783 0.0555 12.2293 0.0000 0.5696 0.7870
#> theta_11 0.8115 0.0486 16.6939 0.0000 0.7162 0.9067
#> theta_22 0.6660 0.0370 18.0193 0.0000 0.5936 0.7385
#> theta_33 0.6553 0.0445 14.7383 0.0000 0.5682 0.7425
#> theta_44 0.6758 0.0472 14.3098 0.0000 0.5832 0.7683
#> mu_11 -0.4208 0.0875 -4.8092 0.0000 -0.5922 -0.2493
#> mu_21 -0.2640 0.0786 -3.3574 0.0008 -0.4181 -0.1099
#> mu_31 -0.3000 0.0816 -3.6778 0.0002 -0.4599 -0.1401
#> mu_41 -0.3142 0.0733 -4.2882 0.0000 -0.4578 -0.1706
#> nu_0 -0.0013 0.1546 -0.0087 0.9930 -0.3044 0.3017
#> alpha_0 -0.4056 0.1117 -3.6325 0.0003 -0.6244 -0.1868
#> kappa_0 0.4159 0.1658 2.5082 0.0121 0.0909 0.7408
#> beta_00 0.8192 0.1502 5.4528 0.0000 0.5248 1.1137
#> gamma_00 0.0853 0.0939 0.9090 0.3633 -0.0987 0.2693
#> gamma_10 0.1172 0.1131 1.0369 0.2998 -0.1044 0.3388
rilta <- FitRILTA2Profiles(
data = data,
ncores = parallel::detectCores(),
starts = c(500, 100),
stiterations = 200,
stscale = 2
)
summary(rilta)
#> est se z p 2.5% 97.5%
#> mu_10 2.2036 0.0838 26.2944 0.0000 2.0393 2.3678
#> mu_20 1.6653 0.0791 21.0455 0.0000 1.5102 1.8204
#> mu_30 1.6534 0.0807 20.5009 0.0000 1.4953 1.8115
#> mu_40 1.3753 0.0703 19.5698 0.0000 1.2375 1.5130
#> lambda_t1 0.8898 0.0775 11.4746 0.0000 0.7378 1.0418
#> lambda_t2 0.8338 0.0696 11.9803 0.0000 0.6974 0.9702
#> lambda_t3 0.8936 0.0698 12.7993 0.0000 0.7567 1.0304
#> lambda_t4 0.6783 0.0555 12.2293 0.0000 0.5696 0.7870
#> theta_11 0.8115 0.0486 16.6939 0.0000 0.7162 0.9067
#> theta_22 0.6660 0.0370 18.0193 0.0000 0.5936 0.7385
#> theta_33 0.6553 0.0445 14.7383 0.0000 0.5682 0.7425
#> theta_44 0.6758 0.0472 14.3098 0.0000 0.5832 0.7683
#> mu_11 -0.4207 0.0875 -4.8091 0.0000 -0.5922 -0.2493
#> mu_21 -0.2640 0.0786 -3.3574 0.0008 -0.4181 -0.1099
#> mu_31 -0.3000 0.0816 -3.6778 0.0002 -0.4599 -0.1401
#> mu_41 -0.3142 0.0733 -4.2882 0.0000 -0.4578 -0.1706
#> nu_0 -0.0014 0.1546 -0.0087 0.9930 -0.3044 0.3017
#> alpha_0 -0.4056 0.1117 -3.6325 0.0003 -0.6244 -0.1868
#> kappa_0 0.4159 0.1658 2.5082 0.0121 0.0909 0.7408
#> beta_00 0.8192 0.1502 5.4528 0.0000 0.5248 1.1137
#> gamma_00 0.0853 0.0939 0.9090 0.3634 -0.0987 0.2693
#> gamma_10 0.1172 0.1131 1.0369 0.2998 -0.1044 0.3388
summary(rilta_starts) - summary(rilta)
#> est se z p 2.5% 97.5%
#> mu_10 0e+00 0 -1e-04 0e+00 0 0
#> mu_20 0e+00 0 0e+00 0e+00 0 0
#> mu_30 0e+00 0 0e+00 0e+00 0 0
#> mu_40 0e+00 0 0e+00 0e+00 0 0
#> lambda_t1 0e+00 0 0e+00 0e+00 0 0
#> lambda_t2 0e+00 0 0e+00 0e+00 0 0
#> lambda_t3 0e+00 0 0e+00 0e+00 0 0
#> lambda_t4 0e+00 0 0e+00 0e+00 0 0
#> theta_11 0e+00 0 0e+00 0e+00 0 0
#> theta_22 0e+00 0 0e+00 0e+00 0 0
#> theta_33 0e+00 0 0e+00 0e+00 0 0
#> theta_44 0e+00 0 0e+00 0e+00 0 0
#> mu_11 -1e-04 0 -1e-04 0e+00 0 0
#> mu_21 0e+00 0 0e+00 0e+00 0 0
#> mu_31 0e+00 0 0e+00 0e+00 0 0
#> mu_41 0e+00 0 0e+00 0e+00 0 0
#> nu_0 1e-04 0 0e+00 0e+00 0 0
#> alpha_0 0e+00 0 0e+00 0e+00 0 0
#> kappa_0 0e+00 0 0e+00 0e+00 0 0
#> beta_00 0e+00 0 0e+00 0e+00 0 0
#> gamma_00 0e+00 0 0e+00 -1e-04 0 0
#> gamma_10 0e+00 0 0e+00 0e+00 0 0The FitCULTA2Profiles function fits the correct
two-profile model using Mplus.
two_profiles_starts <- FitCULTA2Profiles(
data = data,
ncores = parallel::detectCores(),
starts = c(500, 100),
stiterations = 200,
stscale = 2,
starting_values = starting_values
)
summary(two_profiles_starts)
#> est se z p 2.5% 97.5%
#> mu_10 2.1695 0.0815 26.6120 0.0000 2.0097 2.3293
#> mu_20 1.5565 0.0779 19.9825 0.0000 1.4039 1.7092
#> mu_30 1.5795 0.0750 21.0706 0.0000 1.4326 1.7264
#> mu_40 1.1605 0.0697 16.6383 0.0000 1.0238 1.2972
#> lambda_t2 0.9352 0.0958 9.7664 0.0000 0.7475 1.1229
#> lambda_s2 0.9350 0.0408 22.9064 0.0000 0.8550 1.0150
#> lambda_t3 0.9094 0.1310 6.9414 0.0000 0.6526 1.1662
#> lambda_s3 0.9566 0.0459 20.8266 0.0000 0.8666 1.0466
#> lambda_t4 0.6841 0.1047 6.5324 0.0000 0.4788 0.8893
#> lambda_s4 1.0039 0.0452 22.1996 0.0000 0.9152 1.0925
#> theta_11 0.2217 0.0173 12.8373 0.0000 0.1878 0.2555
#> theta_22 0.2296 0.0122 18.8167 0.0000 0.2057 0.2535
#> theta_33 0.2072 0.0124 16.7196 0.0000 0.1829 0.2315
#> theta_44 0.1752 0.0178 9.8303 0.0000 0.1403 0.2101
#> phi_0 -0.0100 0.0669 -0.1490 0.8816 -0.1411 0.1211
#> psi_t 0.4327 0.1040 4.1613 0.0000 0.2289 0.6365
#> psi_p_11 0.2222 0.0485 4.5845 0.0000 0.1272 0.3172
#> psi_p_22 0.2469 0.0382 6.4666 0.0000 0.1721 0.3218
#> psi_p_33 0.2741 0.0500 5.4860 0.0000 0.1762 0.3720
#> psi_p_44 0.3041 0.0450 6.7518 0.0000 0.2158 0.3924
#> psi_s0 1.1565 0.2344 4.9338 0.0000 0.6971 1.6160
#> psi_s 0.4781 0.0639 7.4876 0.0000 0.3530 0.6033
#> mu_11 -0.2860 0.0898 -3.1855 0.0014 -0.4619 -0.1100
#> mu_21 -0.0881 0.0757 -1.1636 0.2446 -0.2365 0.0603
#> mu_31 -0.1545 0.0771 -2.0044 0.0450 -0.3056 -0.0034
#> mu_41 -0.0511 0.0758 -0.6745 0.5000 -0.1996 0.0974
#> phi_1 0.3327 0.0676 4.9230 0.0000 0.2002 0.4651
#> nu_0 -0.2154 0.1909 -1.1282 0.2592 -0.5896 0.1588
#> alpha_0 -0.3451 0.1259 -2.7405 0.0061 -0.5920 -0.0983
#> kappa_0 0.3926 0.2298 1.7083 0.0876 -0.0578 0.8431
#> beta_00 0.6690 0.1680 3.9812 0.0001 0.3396 0.9983
#> gamma_00 0.2315 0.1087 2.1307 0.0331 0.0186 0.4445
#> gamma_10 0.2816 0.1137 2.4767 0.0133 0.0587 0.5044
two_profiles <- FitCULTA2Profiles(
data = data,
ncores = parallel::detectCores(),
starts = c(500, 100),
stiterations = 200,
stscale = 2
)
summary(two_profiles)
#> est se z p 2.5% 97.5%
#> mu_10 2.1695 0.0815 26.6118 0.0000 2.0097 2.3293
#> mu_20 1.5565 0.0779 19.9824 0.0000 1.4039 1.7092
#> mu_30 1.5795 0.0750 21.0706 0.0000 1.4326 1.7264
#> mu_40 1.1605 0.0698 16.6377 0.0000 1.0238 1.2972
#> lambda_t2 0.9352 0.0958 9.7663 0.0000 0.7475 1.1229
#> lambda_s2 0.9350 0.0408 22.9064 0.0000 0.8550 1.0150
#> lambda_t3 0.9094 0.1310 6.9413 0.0000 0.6526 1.1662
#> lambda_s3 0.9566 0.0459 20.8264 0.0000 0.8666 1.0466
#> lambda_t4 0.6841 0.1047 6.5324 0.0000 0.4788 0.8893
#> lambda_s4 1.0039 0.0452 22.1997 0.0000 0.9152 1.0925
#> theta_11 0.2217 0.0173 12.8371 0.0000 0.1878 0.2555
#> theta_22 0.2296 0.0122 18.8169 0.0000 0.2057 0.2535
#> theta_33 0.2072 0.0124 16.7196 0.0000 0.1829 0.2315
#> theta_44 0.1752 0.0178 9.8294 0.0000 0.1403 0.2101
#> phi_0 -0.0100 0.0669 -0.1489 0.8817 -0.1411 0.1212
#> psi_t 0.4327 0.1040 4.1612 0.0000 0.2289 0.6365
#> psi_p_11 0.2222 0.0485 4.5845 0.0000 0.1272 0.3172
#> psi_p_22 0.2469 0.0382 6.4665 0.0000 0.1721 0.3218
#> psi_p_33 0.2741 0.0500 5.4859 0.0000 0.1762 0.3720
#> psi_p_44 0.3041 0.0450 6.7518 0.0000 0.2158 0.3924
#> psi_s0 1.1566 0.2344 4.9337 0.0000 0.6971 1.6160
#> psi_s 0.4781 0.0639 7.4873 0.0000 0.3530 0.6033
#> mu_11 -0.2859 0.0898 -3.1853 0.0014 -0.4619 -0.1100
#> mu_21 -0.0881 0.0757 -1.1634 0.2447 -0.2365 0.0603
#> mu_31 -0.1545 0.0771 -2.0043 0.0450 -0.3056 -0.0034
#> mu_41 -0.0511 0.0758 -0.6742 0.5002 -0.1996 0.0974
#> phi_1 0.3327 0.0676 4.9230 0.0000 0.2002 0.4651
#> nu_0 -0.2154 0.1909 -1.1283 0.2592 -0.5896 0.1588
#> alpha_0 -0.3451 0.1259 -2.7405 0.0061 -0.5920 -0.0983
#> kappa_0 0.3926 0.2298 1.7083 0.0876 -0.0578 0.8431
#> beta_00 0.6690 0.1680 3.9811 0.0001 0.3396 0.9983
#> gamma_00 0.2315 0.1087 2.1308 0.0331 0.0186 0.4445
#> gamma_10 0.2816 0.1137 2.4768 0.0133 0.0588 0.5044
summary(two_profiles_starts) - summary(two_profiles)
#> est se z p 2.5% 97.5%
#> mu_10 0e+00 0e+00 2e-04 0e+00 0e+00 0e+00
#> mu_20 0e+00 0e+00 1e-04 0e+00 0e+00 0e+00
#> mu_30 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00
#> mu_40 0e+00 -1e-04 6e-04 0e+00 0e+00 0e+00
#> lambda_t2 0e+00 0e+00 1e-04 0e+00 0e+00 0e+00
#> lambda_s2 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00
#> lambda_t3 0e+00 0e+00 1e-04 0e+00 0e+00 0e+00
#> lambda_s3 0e+00 0e+00 2e-04 0e+00 0e+00 0e+00
#> lambda_t4 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00
#> lambda_s4 0e+00 0e+00 -1e-04 0e+00 0e+00 0e+00
#> theta_11 0e+00 0e+00 2e-04 0e+00 0e+00 0e+00
#> theta_22 0e+00 0e+00 -2e-04 0e+00 0e+00 0e+00
#> theta_33 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00
#> theta_44 0e+00 0e+00 9e-04 0e+00 0e+00 0e+00
#> phi_0 0e+00 0e+00 -1e-04 -1e-04 0e+00 -1e-04
#> psi_t 0e+00 0e+00 1e-04 0e+00 0e+00 0e+00
#> psi_p_11 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00
#> psi_p_22 0e+00 0e+00 1e-04 0e+00 0e+00 0e+00
#> psi_p_33 0e+00 0e+00 1e-04 0e+00 0e+00 0e+00
#> psi_p_44 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00
#> psi_s0 -1e-04 0e+00 1e-04 0e+00 0e+00 0e+00
#> psi_s 0e+00 0e+00 3e-04 0e+00 0e+00 0e+00
#> mu_11 -1e-04 0e+00 -2e-04 0e+00 0e+00 0e+00
#> mu_21 0e+00 0e+00 -2e-04 -1e-04 0e+00 0e+00
#> mu_31 0e+00 0e+00 -1e-04 0e+00 0e+00 0e+00
#> mu_41 0e+00 0e+00 -3e-04 -2e-04 0e+00 0e+00
#> phi_1 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00
#> nu_0 0e+00 0e+00 1e-04 0e+00 0e+00 0e+00
#> alpha_0 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00
#> kappa_0 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00
#> beta_00 0e+00 0e+00 1e-04 0e+00 0e+00 0e+00
#> gamma_00 0e+00 0e+00 -1e-04 0e+00 0e+00 0e+00
#> gamma_10 0e+00 0e+00 -1e-04 0e+00 -1e-04 0e+00