Estimates the parameters of a model created using the slca function.
Usage
estimate(x, ...)
# S3 method for class 'slca'
estimate(x,
data,
method = c("em", "hybrid", "nlm"),
fix2zero = NULL,
control = slcaControl(), ...)Arguments
- x
an
slcaobject defining theslcamodel to be estimated.- ...
additional arguments passed to the estimation process.
- data
a
data.framecontaining the observed categorical variables included in the model.- method
a character string specifying the estimation method for SLCM parameters. The default is
"em", which uses the expectation-maximization (EM) algorithm. The alternative"nlm"employs the Newton-Raphson algorithm via thenlmfunction, while"hybrid"combines both approaches, starting with EM and finishing withnlmfor refined estimates.- fix2zero
a
vectorspecifying parameters to be constrained to zero. See the 'Details' section for further information.- control
a
listof control parameters for the estimation procedure. Modify default values usingslcaControl().
Value
An object of class slcafit containing the following components:
- model
a
listdescribing of the model structure.- method
the estimation method used.
- arg
a brief description of the model used during estimation.
- mf
the
data.frameused for estimation.- par
the log of the estimated paramters.
- logit
the log-odds of the estimated parameters.
- score
the score function for the estimated parameters.
- posterior
a
listof posterior probablities for each latent class variable.- convergence
a logical indicator of whether convergence was achieved.
- loglikelihood
the loglikelihood value of the estimated model.
- control
the control settings used during the estimation process.
The returned object can be further processed using the param function to extract the estimated parameters or their standard errors. The regress function allows for logistic regression analysis using a three-step approach to evaluate the effects of external variables on latent class variables. Additionally, several other methods are available, including predict.slcafit, reorder.slcafit, gof, and others.
Details
The fix2zero argument allows you to constrain specific parameters to zero. Each parameter is associated with a unique index, which can be identified using the param function with the argument index = TRUE. To apply constraints, provide the relevant parameter indices in the fix2zero arguments with vector.
Examples
m <- slca(lc[3] ~ y1 + y2 + y3 + y4)
pi <- rep(1 / 3, 3)
rho <- c(.9, .1, .9, .1, .9, .1, .9, .1, # class 1
.9, .1, .9, .1, .1, .9, .1, .9, # class 2
.1, .9, .1, .9, .1, .9, .1, .9) # class 3
dt <- simulate(m, 200, parm = c(pi, rho))
estimate(m, dt$response)
#> Structural Latent Variable Model
#>
#> Latent variables (Root*):
#> Label: lc*
#> nclass: 3
#>
#> Measurement model:
#> lc -> { y1, y2, y3, y4 } a
#>
#> LogLik: -396.1722
# Several estimation methods
estimate(m, dt$response, method = "em",
control = slcaControl(verbose = TRUE)) # default
#> EM iteration begin.
#> 1 iterations logLik: -555.07 diff: inf
2 iterations logLik: -511.98 diff: 43.08609
3 iterations logLik: -509.90 diff: 2.08325
4 iterations logLik: -500.10 diff: 9.80122
5 iterations logLik: -470.22 diff: 29.88096
6 iterations logLik: -437.56 diff: 32.65298
7 iterations logLik: -423.55 diff: 14.01664
8 iterations logLik: -411.63 diff: 11.91095
9 iterations logLik: -401.67 diff: 9.96603
10 iterations logLik: -398.19 diff: 3.48230
11 iterations logLik: -397.69 diff: 0.49546
12 iterations logLik: -397.64 diff: 0.04873
13 iterations logLik: -397.63 diff: 0.01264
14 iterations logLik: -397.62 diff: 0.01098
15 iterations logLik: -397.61 diff: 0.01176
16 iterations logLik: -397.59 diff: 0.01279
17 iterations logLik: -397.58 diff: 0.01394
18 iterations logLik: -397.56 diff: 0.01520
19 iterations logLik: -397.55 diff: 0.01658
20 iterations logLik: -397.53 diff: 0.01807
21 iterations logLik: -397.51 diff: 0.01969
22 iterations logLik: -397.49 diff: 0.02143
23 iterations logLik: -397.47 diff: 0.02328
24 iterations logLik: -397.44 diff: 0.02523
25 iterations logLik: -397.41 diff: 0.02726
26 iterations logLik: -397.38 diff: 0.02936
27 iterations logLik: -397.35 diff: 0.03149
28 iterations logLik: -397.32 diff: 0.03361
29 iterations logLik: -397.28 diff: 0.03569
30 iterations logLik: -397.25 diff: 0.03767
31 iterations logLik: -397.21 diff: 0.03952
32 iterations logLik: -397.16 diff: 0.04117
33 iterations logLik: -397.12 diff: 0.04259
34 iterations logLik: -397.08 diff: 0.04373
35 iterations logLik: -397.03 diff: 0.04456
36 iterations logLik: -396.99 diff: 0.04507
37 iterations logLik: -396.94 diff: 0.04522
38 iterations logLik: -396.90 diff: 0.04504
39 iterations logLik: -396.85 diff: 0.04453
40 iterations logLik: -396.81 diff: 0.04371
41 iterations logLik: -396.77 diff: 0.04261
42 iterations logLik: -396.73 diff: 0.04127
43 iterations logLik: -396.69 diff: 0.03972
44 iterations logLik: -396.65 diff: 0.03801
45 iterations logLik: -396.61 diff: 0.03617
46 iterations logLik: -396.58 diff: 0.03424
47 iterations logLik: -396.55 diff: 0.03226
48 iterations logLik: -396.52 diff: 0.03027
49 iterations logLik: -396.49 diff: 0.02828
50 iterations logLik: -396.46 diff: 0.02633
51 iterations logLik: -396.44 diff: 0.02443
52 iterations logLik: -396.41 diff: 0.02259
53 iterations logLik: -396.39 diff: 0.02084
54 iterations logLik: -396.37 diff: 0.01918
55 iterations logLik: -396.36 diff: 0.01761
56 iterations logLik: -396.34 diff: 0.01613
57 iterations logLik: -396.33 diff: 0.01476
58 iterations logLik: -396.31 diff: 0.01348
59 iterations logLik: -396.30 diff: 0.01229
60 iterations logLik: -396.29 diff: 0.01120
61 iterations logLik: -396.28 diff: 0.01020
62 iterations logLik: -396.27 diff: 0.00928
63 iterations logLik: -396.26 diff: 0.00843
64 iterations logLik: -396.25 diff: 0.00766
65 iterations logLik: -396.25 diff: 0.00696
66 iterations logLik: -396.24 diff: 0.00632
67 iterations logLik: -396.23 diff: 0.00574
68 iterations logLik: -396.23 diff: 0.00521
69 iterations logLik: -396.22 diff: 0.00473
70 iterations logLik: -396.22 diff: 0.00429
71 iterations logLik: -396.22 diff: 0.00390
72 iterations logLik: -396.21 diff: 0.00354
73 iterations logLik: -396.21 diff: 0.00322
74 iterations logLik: -396.21 diff: 0.00292
75 iterations logLik: -396.20 diff: 0.00266
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85 iterations logLik: -396.19 diff: 0.00106
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88 iterations logLik: -396.18 diff: 0.00082
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90 iterations logLik: -396.18 diff: 0.00069
91 iterations logLik: -396.18 diff: 0.00063
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99 iterations logLik: -396.18 diff: 0.00034
100 iterations logLik: -396.18 diff: 0.00031
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104 iterations logLik: -396.18 diff: 0.00024
105 iterations logLik: -396.18 diff: 0.00022
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107 iterations logLik: -396.18 diff: 0.00019
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110 iterations logLik: -396.18 diff: 0.00016
111 iterations logLik: -396.18 diff: 0.00015
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113 iterations logLik: -396.18 diff: 0.00013
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115 iterations logLik: -396.18 diff: 0.00012
116 iterations logLik: -396.18 diff: 0.00011
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118 iterations logLik: -396.18 diff: 0.00010
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120 iterations logLik: -396.18 diff: 0.00009
121 iterations logLik: -396.18 diff: 0.00009
122 iterations logLik: -396.18 diff: 0.00008
123 iterations logLik: -396.17 diff: 0.00008
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145 iterations logLik: -396.17 diff: 0.00003
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150 iterations logLik: -396.17 diff: 0.00003
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154 iterations logLik: -396.17 diff: 0.00003
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156 iterations logLik: -396.17 diff: 0.00002
157 iterations logLik: -396.17 diff: 0.00002
158 iterations logLik: -396.17 diff: 0.00002
159 iterations logLik: -396.17 diff: 0.00002
160 iterations logLik: -396.17 diff: 0.00002
161 iterations logLik: -396.17 diff: 0.00002
162 iterations logLik: -396.17 diff: 0.00002
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201 iterations logLik: -396.17 diff: 9.7e-06
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792 iterations logLik: -396.17 diff: 1.2e-08
793 iterations logLik: -396.17 diff: 1.2e-08
794 iterations logLik: -396.17 diff: 1.2e-08
795 iterations logLik: -396.17 diff: 1.2e-08
796 iterations logLik: -396.17 diff: 1.2e-08
797 iterations logLik: -396.17 diff: 1.2e-08
798 iterations logLik: -396.17 diff: 1.2e-08
799 iterations logLik: -396.17 diff: 1.1e-08
800 iterations logLik: -396.17 diff: 1.1e-08
801 iterations logLik: -396.17 diff: 1.1e-08
802 iterations logLik: -396.17 diff: 1.1e-08
803 iterations logLik: -396.17 diff: 1.1e-08
804 iterations logLik: -396.17 diff: 1.1e-08
805 iterations logLik: -396.17 diff: 1.1e-08
806 iterations logLik: -396.17 diff: 1.1e-08
807 iterations logLik: -396.17 diff: 1.1e-08
808 iterations logLik: -396.17 diff: 1.0e-08
809 iterations logLik: -396.17 diff: 1.0e-08
810 iterations logLik: -396.17 diff: 1.0e-08
811 iterations logLik: -396.17 diff: 1.0e-08
812 iterations logLik: -396.17 diff: 1.0e-08
813 iterations logLik: -396.17 diff: 1.0e-08
#> .. done.
#> Structural Latent Variable Model
#>
#> Latent variables (Root*):
#> Label: lc*
#> nclass: 3
#>
#> Measurement model:
#> lc -> { y1, y2, y3, y4 } a
#>
#> LogLik: -396.1722
estimate(m, dt$response, method = "nlm",
control = slcaControl(verbose = TRUE))
#> nlm iteration begin.
#> .. done.
#> Structural Latent Variable Model
#>
#> Latent variables (Root*):
#> Label: lc*
#> nclass: 3
#>
#> Measurement model:
#> lc -> { y1, y2, y3, y4 } a
#>
#> LogLik: -396.1722
estimate(m, dt$response, method = "hybrid",
control = slcaControl(verbose = TRUE))
#> EM iteration begin.
#> 1 iterations logLik: -555.41 diff: inf
2 iterations logLik: -512.40 diff: 43.00670
3 iterations logLik: -512.18 diff: 0.22563
4 iterations logLik: -510.99 diff: 1.18797
5 iterations logLik: -505.07 diff: 5.92316
6 iterations logLik: -482.78 diff: 22.28088
7 iterations logLik: -446.04 diff: 36.74039
8 iterations logLik: -428.90 diff: 17.14771
9 iterations logLik: -419.91 diff: 8.98238
10 iterations logLik: -408.31 diff: 11.60348
11 iterations logLik: -400.08 diff: 8.23315
12 iterations logLik: -397.76 diff: 2.32009
13 iterations logLik: -397.45 diff: 0.30874
14 iterations logLik: -397.40 diff: 0.04823
15 iterations logLik: -397.37 diff: 0.02836
16 iterations logLik: -397.34 diff: 0.02808
17 iterations logLik: -397.32 diff: 0.02913
18 iterations logLik: -397.28 diff: 0.03025
19 iterations logLik: -397.25 diff: 0.03136
20 iterations logLik: -397.22 diff: 0.03243
21 iterations logLik: -397.19 diff: 0.03346
22 iterations logLik: -397.15 diff: 0.03442
23 iterations logLik: -397.12 diff: 0.03530
24 iterations logLik: -397.08 diff: 0.03610
25 iterations logLik: -397.05 diff: 0.03678
26 iterations logLik: -397.01 diff: 0.03733
27 iterations logLik: -396.97 diff: 0.03773
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31 iterations logLik: -396.82 diff: 0.03732
32 iterations logLik: -396.78 diff: 0.03665
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37 iterations logLik: -396.62 diff: 0.03013
38 iterations logLik: -396.59 diff: 0.02841
39 iterations logLik: -396.56 diff: 0.02664
40 iterations logLik: -396.54 diff: 0.02487
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157 iterations logLik: -396.18 diff: 0.00013
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162 iterations logLik: -396.18 diff: 0.00011
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164 iterations logLik: -396.18 diff: 0.00010
165 iterations logLik: -396.18 diff: 0.00010
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168 iterations logLik: -396.18 diff: 0.00009
169 iterations logLik: -396.18 diff: 0.00009
170 iterations logLik: -396.18 diff: 0.00009
171 iterations logLik: -396.18 diff: 0.00008
172 iterations logLik: -396.18 diff: 0.00008
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805 iterations logLik: -396.17 diff: 2.0e-08
806 iterations logLik: -396.17 diff: 2.0e-08
807 iterations logLik: -396.17 diff: 2.0e-08
808 iterations logLik: -396.17 diff: 1.9e-08
809 iterations logLik: -396.17 diff: 1.9e-08
810 iterations logLik: -396.17 diff: 1.9e-08
811 iterations logLik: -396.17 diff: 1.9e-08
812 iterations logLik: -396.17 diff: 1.9e-08
813 iterations logLik: -396.17 diff: 1.8e-08
814 iterations logLik: -396.17 diff: 1.8e-08
815 iterations logLik: -396.17 diff: 1.8e-08
816 iterations logLik: -396.17 diff: 1.8e-08
817 iterations logLik: -396.17 diff: 1.8e-08
818 iterations logLik: -396.17 diff: 1.8e-08
819 iterations logLik: -396.17 diff: 1.7e-08
820 iterations logLik: -396.17 diff: 1.7e-08
821 iterations logLik: -396.17 diff: 1.7e-08
822 iterations logLik: -396.17 diff: 1.7e-08
823 iterations logLik: -396.17 diff: 1.7e-08
824 iterations logLik: -396.17 diff: 1.7e-08
825 iterations logLik: -396.17 diff: 1.6e-08
826 iterations logLik: -396.17 diff: 1.6e-08
827 iterations logLik: -396.17 diff: 1.6e-08
828 iterations logLik: -396.17 diff: 1.6e-08
829 iterations logLik: -396.17 diff: 1.6e-08
830 iterations logLik: -396.17 diff: 1.6e-08
831 iterations logLik: -396.17 diff: 1.6e-08
832 iterations logLik: -396.17 diff: 1.5e-08
833 iterations logLik: -396.17 diff: 1.5e-08
834 iterations logLik: -396.17 diff: 1.5e-08
835 iterations logLik: -396.17 diff: 1.5e-08
836 iterations logLik: -396.17 diff: 1.5e-08
837 iterations logLik: -396.17 diff: 1.5e-08
838 iterations logLik: -396.17 diff: 1.5e-08
839 iterations logLik: -396.17 diff: 1.4e-08
840 iterations logLik: -396.17 diff: 1.4e-08
841 iterations logLik: -396.17 diff: 1.4e-08
842 iterations logLik: -396.17 diff: 1.4e-08
843 iterations logLik: -396.17 diff: 1.4e-08
844 iterations logLik: -396.17 diff: 1.4e-08
845 iterations logLik: -396.17 diff: 1.4e-08
846 iterations logLik: -396.17 diff: 1.3e-08
847 iterations logLik: -396.17 diff: 1.3e-08
848 iterations logLik: -396.17 diff: 1.3e-08
849 iterations logLik: -396.17 diff: 1.3e-08
850 iterations logLik: -396.17 diff: 1.3e-08
851 iterations logLik: -396.17 diff: 1.3e-08
852 iterations logLik: -396.17 diff: 1.3e-08
853 iterations logLik: -396.17 diff: 1.3e-08
854 iterations logLik: -396.17 diff: 1.2e-08
855 iterations logLik: -396.17 diff: 1.2e-08
856 iterations logLik: -396.17 diff: 1.2e-08
857 iterations logLik: -396.17 diff: 1.2e-08
858 iterations logLik: -396.17 diff: 1.2e-08
859 iterations logLik: -396.17 diff: 1.2e-08
860 iterations logLik: -396.17 diff: 1.2e-08
861 iterations logLik: -396.17 diff: 1.2e-08
862 iterations logLik: -396.17 diff: 1.2e-08
863 iterations logLik: -396.17 diff: 1.1e-08
864 iterations logLik: -396.17 diff: 1.1e-08
865 iterations logLik: -396.17 diff: 1.1e-08
866 iterations logLik: -396.17 diff: 1.1e-08
867 iterations logLik: -396.17 diff: 1.1e-08
868 iterations logLik: -396.17 diff: 1.1e-08
869 iterations logLik: -396.17 diff: 1.1e-08
870 iterations logLik: -396.17 diff: 1.1e-08
871 iterations logLik: -396.17 diff: 1.1e-08
872 iterations logLik: -396.17 diff: 1.0e-08
873 iterations logLik: -396.17 diff: 1.0e-08
874 iterations logLik: -396.17 diff: 1.0e-08
875 iterations logLik: -396.17 diff: 1.0e-08
876 iterations logLik: -396.17 diff: 1.0e-08
877 iterations logLik: -396.17 diff: 1.0e-08
#> .. done.
#> nlm iteration begin.
#> .. done.
#> Structural Latent Variable Model
#>
#> Latent variables (Root*):
#> Label: lc*
#> nclass: 3
#>
#> Measurement model:
#> lc -> { y1, y2, y3, y4 } a
#>
#> LogLik: -396.1722
# Parameter restriction
mf <- estimate(m, dt$response)
param(mf, index = TRUE)
#> PI :
#> (lc)
#> class
#> 1 2 3
#> 0.3123 (1) 0.3295 (2) 0.3582 (3)
#>
#> RHO :
#> (a)
#> class
#> response 1 2 3
#> 1(V1) 0.1678 (4) 0.9689 (12) 0.8329 (20)
#> 2 0.8322 (5) 0.0311 (13) 0.1671 (21)
#> 1(V2) 0.0000 (6) 0.9463 (14) 1.0000 (22)
#> 2 1.0000 (7) 0.0537 (15) 0.0000 (23)
#> 1(V3) 0.0492 (8) 0.8358 (16) 0.1235 (24)
#> 2 0.9508 (9) 0.1642 (17) 0.8765 (25)
#> 1(V4) 0.1357 (10) 0.9791 (18) 0.0000 (26)
#> 2 0.8643 (11) 0.0209 (19) 1.0000 (27)
#>
#> V1 V2 V3 V4
#> lc y1 y2 y3 y4
mf0 <- estimate(mf, fix2zero = c(4, 6, 8, 10))
param(mf0)
#> PI :
#> (lc)
#> class
#> 1 2 3
#> 0.2005 0.4529 0.3466
#>
#> RHO :
#> (a)
#> class
#> response 1 2 3
#> 1(V1) 0.0000 0.8488 0.8239
#> 2 1.0000 0.1512 0.1761
#> 1(V2) 0.0000 0.8256 0.8543
#> 2 1.0000 0.1744 0.1457
#> 1(V3) 0.0000 0.7397 0.0000
#> 2 1.0000 0.2603 1.0000
#> 1(V4) 0.0000 0.8060 0.0000
#> 2 1.0000 0.1940 1.0000
#>
#> V1 V2 V3 V4
#> lc y1 y2 y3 y4
# Estimation control
estimate(m, dt$response, control = slcaControl(nrep = 3, verbose = TRUE))
#> Inital parameter test:
#> 1 / 3 logLik: -396.1722
#> 2 / 3 logLik: -396.1722
#> 3 / 3 logLik: -396.1722
#>
#> 1th parameter set has been selected.
#>
#> EM iteration begin.
#> 1 iterations logLik: -396.17 diff: inf
2 iterations logLik: -396.17 diff: 8.3e-09
#> .. done.
#> Structural Latent Variable Model
#>
#> Latent variables (Root*):
#> Label: lc*
#> nclass: 3
#>
#> Measurement model:
#> lc -> { y1, y2, y3, y4 } a
#>
#> LogLik: -396.1722
estimate(m, dt$response, control = slcaControl(init.param = c(pi, rho)))
#> Structural Latent Variable Model
#>
#> Latent variables (Root*):
#> Label: lc*
#> nclass: 3
#>
#> Measurement model:
#> lc -> { y1, y2, y3, y4 } a
#>
#> LogLik: -396.1722