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. When re-estimating a fitted object, an omitted argument retains its existing constraints; explicitly supplyingNULLremoves the constraint specification. 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 named logical vector indicating whether convergence was achieved for the EM and
nlmsteps. Steps not used by the selected method are returned asNA.- 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.
Manifest responses are categorical; continuous-response models are not
supported. Corresponding indicators under equality constraints must have
identical factor levels, including labels and order. For categories absent
from a sample, declare the full levels explicitly, for example
factor(x, levels = 1:3), consistently across constrained indicators.
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$response)
#> Structural Latent Variable Model
#>
#> Latent variables (Root*):
#> Label: lc*
#> nclass: 3
#>
#> Measurement model:
#> lc -> { y1, y2, y3, y4 } a
#>
#> LogLik: -418.9054
# Several estimation methods
estimate(m, dt$response, method = "em",
control = slcaControl(verbose = TRUE)) # default
#> EM iteration begin.
#> 1 iterations logLik: -554.54 diff: inf
2 iterations logLik: -533.79 diff: 20.74630
3 iterations logLik: -530.51 diff: 3.28618
4 iterations logLik: -515.22 diff: 15.28819
5 iterations logLik: -475.98 diff: 39.23392
6 iterations logLik: -446.04 diff: 29.94218
7 iterations logLik: -436.56 diff: 9.48504
8 iterations logLik: -429.55 diff: 7.00494
9 iterations logLik: -423.13 diff: 6.41722
10 iterations logLik: -419.85 diff: 3.27974
11 iterations logLik: -419.09 diff: 0.76023
12 iterations logLik: -419.00 diff: 0.09750
13 iterations logLik: -418.99 diff: 0.01031
14 iterations logLik: -418.99 diff: 0.00156
15 iterations logLik: -418.98 diff: 0.00070
16 iterations logLik: -418.98 diff: 0.00063
17 iterations logLik: -418.98 diff: 0.00064
18 iterations logLik: -418.98 diff: 0.00066
19 iterations logLik: -418.98 diff: 0.00068
20 iterations logLik: -418.98 diff: 0.00070
21 iterations logLik: -418.98 diff: 0.00072
22 iterations logLik: -418.98 diff: 0.00074
23 iterations logLik: -418.98 diff: 0.00076
24 iterations logLik: -418.98 diff: 0.00078
25 iterations logLik: -418.98 diff: 0.00081
26 iterations logLik: -418.98 diff: 0.00083
27 iterations logLik: -418.98 diff: 0.00086
28 iterations logLik: -418.97 diff: 0.00088
29 iterations logLik: -418.97 diff: 0.00091
30 iterations logLik: -418.97 diff: 0.00093
31 iterations logLik: -418.97 diff: 0.00096
32 iterations logLik: -418.97 diff: 0.00099
33 iterations logLik: -418.97 diff: 0.00101
34 iterations logLik: -418.97 diff: 0.00104
35 iterations logLik: -418.97 diff: 0.00107
36 iterations logLik: -418.97 diff: 0.00110
37 iterations logLik: -418.97 diff: 0.00113
38 iterations logLik: -418.96 diff: 0.00116
39 iterations logLik: -418.96 diff: 0.00119
40 iterations logLik: -418.96 diff: 0.00122
41 iterations logLik: -418.96 diff: 0.00125
42 iterations logLik: -418.96 diff: 0.00128
43 iterations logLik: -418.96 diff: 0.00131
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50 iterations logLik: -418.95 diff: 0.00152
51 iterations logLik: -418.95 diff: 0.00155
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55 iterations logLik: -418.94 diff: 0.00166
56 iterations logLik: -418.94 diff: 0.00168
57 iterations logLik: -418.94 diff: 0.00171
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59 iterations logLik: -418.93 diff: 0.00176
60 iterations logLik: -418.93 diff: 0.00178
61 iterations logLik: -418.93 diff: 0.00180
62 iterations logLik: -418.93 diff: 0.00182
63 iterations logLik: -418.93 diff: 0.00184
64 iterations logLik: -418.92 diff: 0.00186
65 iterations logLik: -418.92 diff: 0.00187
66 iterations logLik: -418.92 diff: 0.00189
67 iterations logLik: -418.92 diff: 0.00190
68 iterations logLik: -418.92 diff: 0.00192
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70 iterations logLik: -418.91 diff: 0.00194
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100 iterations logLik: -418.86 diff: 0.00156
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160 iterations logLik: -418.81 diff: 0.00029
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172 iterations logLik: -418.81 diff: 0.00019
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174 iterations logLik: -418.81 diff: 0.00018
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799 iterations logLik: -418.80 diff: 2.2e-08
800 iterations logLik: -418.80 diff: 2.1e-08
801 iterations logLik: -418.80 diff: 2.1e-08
802 iterations logLik: -418.80 diff: 2.1e-08
803 iterations logLik: -418.80 diff: 2.0e-08
804 iterations logLik: -418.80 diff: 2.0e-08
805 iterations logLik: -418.80 diff: 2.0e-08
806 iterations logLik: -418.80 diff: 1.9e-08
807 iterations logLik: -418.80 diff: 1.9e-08
808 iterations logLik: -418.80 diff: 1.9e-08
809 iterations logLik: -418.80 diff: 1.9e-08
810 iterations logLik: -418.80 diff: 1.8e-08
811 iterations logLik: -418.80 diff: 1.8e-08
812 iterations logLik: -418.80 diff: 1.8e-08
813 iterations logLik: -418.80 diff: 1.8e-08
814 iterations logLik: -418.80 diff: 1.7e-08
815 iterations logLik: -418.80 diff: 1.7e-08
816 iterations logLik: -418.80 diff: 1.7e-08
817 iterations logLik: -418.80 diff: 1.7e-08
818 iterations logLik: -418.80 diff: 1.6e-08
819 iterations logLik: -418.80 diff: 1.6e-08
820 iterations logLik: -418.80 diff: 1.6e-08
821 iterations logLik: -418.80 diff: 1.6e-08
822 iterations logLik: -418.80 diff: 1.6e-08
823 iterations logLik: -418.80 diff: 1.5e-08
824 iterations logLik: -418.80 diff: 1.5e-08
825 iterations logLik: -418.80 diff: 1.5e-08
826 iterations logLik: -418.80 diff: 1.5e-08
827 iterations logLik: -418.80 diff: 1.4e-08
828 iterations logLik: -418.80 diff: 1.4e-08
829 iterations logLik: -418.80 diff: 1.4e-08
830 iterations logLik: -418.80 diff: 1.4e-08
831 iterations logLik: -418.80 diff: 1.4e-08
832 iterations logLik: -418.80 diff: 1.3e-08
833 iterations logLik: -418.80 diff: 1.3e-08
834 iterations logLik: -418.80 diff: 1.3e-08
835 iterations logLik: -418.80 diff: 1.3e-08
836 iterations logLik: -418.80 diff: 1.3e-08
837 iterations logLik: -418.80 diff: 1.3e-08
838 iterations logLik: -418.80 diff: 1.2e-08
839 iterations logLik: -418.80 diff: 1.2e-08
840 iterations logLik: -418.80 diff: 1.2e-08
841 iterations logLik: -418.80 diff: 1.2e-08
842 iterations logLik: -418.80 diff: 1.2e-08
843 iterations logLik: -418.80 diff: 1.1e-08
844 iterations logLik: -418.80 diff: 1.1e-08
845 iterations logLik: -418.80 diff: 1.1e-08
846 iterations logLik: -418.80 diff: 1.1e-08
847 iterations logLik: -418.80 diff: 1.1e-08
848 iterations logLik: -418.80 diff: 1.1e-08
849 iterations logLik: -418.80 diff: 1.1e-08
850 iterations logLik: -418.80 diff: 1.0e-08
851 iterations logLik: -418.80 diff: 1.0e-08
852 iterations logLik: -418.80 diff: 1.0e-08
853 iterations logLik: -418.80 diff: 9.9e-09
#> .. done.
#> Structural Latent Variable Model
#>
#> Latent variables (Root*):
#> Label: lc*
#> nclass: 3
#>
#> Measurement model:
#> lc -> { y1, y2, y3, y4 } a
#>
#> LogLik: -418.7988
estimate(m, dt$response, method = "nlm",
control = slcaControl(verbose = TRUE))
#> nlm iteration begin.
#> .. done.
#> Structural Latent Variable Model
#>
#> Latent variables (Root*):
#> Label: lc*
#> nclass: 3
#>
#> Measurement model:
#> lc -> { y1, y2, y3, y4 } a
#>
#> LogLik: -418.7988
estimate(m, dt$response, method = "hybrid",
control = slcaControl(verbose = TRUE))
#> EM iteration begin.
#> 1 iterations logLik: -554.54 diff: inf
2 iterations logLik: -534.38 diff: 20.16155
3 iterations logLik: -533.72 diff: 0.65777
4 iterations logLik: -530.13 diff: 3.59115
5 iterations logLik: -513.55 diff: 16.58633
6 iterations logLik: -473.07 diff: 40.47730
7 iterations logLik: -445.36 diff: 27.71048
8 iterations logLik: -436.43 diff: 8.93181
9 iterations logLik: -428.50 diff: 7.92164
10 iterations logLik: -422.17 diff: 6.33631
11 iterations logLik: -419.56 diff: 2.60347
12 iterations logLik: -419.04 diff: 0.52411
13 iterations logLik: -418.98 diff: 0.06414
14 iterations logLik: -418.97 diff: 0.00653
15 iterations logLik: -418.97 diff: 0.00091
16 iterations logLik: -418.97 diff: 0.00041
17 iterations logLik: -418.97 diff: 0.00036
18 iterations logLik: -418.97 diff: 0.00036
19 iterations logLik: -418.97 diff: 0.00036
20 iterations logLik: -418.97 diff: 0.00036
21 iterations logLik: -418.97 diff: 0.00035
22 iterations logLik: -418.97 diff: 0.00035
23 iterations logLik: -418.97 diff: 0.00035
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25 iterations logLik: -418.97 diff: 0.00035
26 iterations logLik: -418.97 diff: 0.00035
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31 iterations logLik: -418.96 diff: 0.00034
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80 iterations logLik: -418.95 diff: 0.00019
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109 iterations logLik: -418.95 diff: 0.00011
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120 iterations logLik: -418.94 diff: 0.00009
121 iterations logLik: -418.94 diff: 0.00009
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143 iterations logLik: -418.94 diff: 0.00006
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150 iterations logLik: -418.94 diff: 0.00006
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154 iterations logLik: -418.94 diff: 0.00005
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170 iterations logLik: -418.94 diff: 0.00005
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172 iterations logLik: -418.94 diff: 0.00004
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#> 1001 iterations logLik: -418.91 diff: 1.7e-06
1002 iterations logLik: -418.91 diff: 1.6e-06
1003 iterations logLik: -418.91 diff: 1.6e-06
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1999 iterations logLik: -418.91 diff: 1.6e-08
2000 iterations logLik: -418.91 diff: 1.6e-08
#> 2001 iterations logLik: -418.91 diff: 1.6e-08
2002 iterations logLik: -418.91 diff: 1.6e-08
2003 iterations logLik: -418.91 diff: 1.6e-08
2004 iterations logLik: -418.91 diff: 1.6e-08
2005 iterations logLik: -418.91 diff: 1.6e-08
2006 iterations logLik: -418.91 diff: 1.6e-08
2007 iterations logLik: -418.91 diff: 1.6e-08
2008 iterations logLik: -418.91 diff: 1.6e-08
2009 iterations logLik: -418.91 diff: 1.6e-08
2010 iterations logLik: -418.91 diff: 1.6e-08
2011 iterations logLik: -418.91 diff: 1.6e-08
2012 iterations logLik: -418.91 diff: 1.6e-08
2013 iterations logLik: -418.91 diff: 1.5e-08
2014 iterations logLik: -418.91 diff: 1.5e-08
2015 iterations logLik: -418.91 diff: 1.5e-08
2016 iterations logLik: -418.91 diff: 1.5e-08
2017 iterations logLik: -418.91 diff: 1.5e-08
2018 iterations logLik: -418.91 diff: 1.5e-08
2019 iterations logLik: -418.91 diff: 1.5e-08
2020 iterations logLik: -418.91 diff: 1.5e-08
2021 iterations logLik: -418.91 diff: 1.5e-08
2022 iterations logLik: -418.91 diff: 1.5e-08
2023 iterations logLik: -418.91 diff: 1.5e-08
2024 iterations logLik: -418.91 diff: 1.5e-08
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2027 iterations logLik: -418.91 diff: 1.5e-08
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2100 iterations logLik: -418.91 diff: 1.2e-08
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2110 iterations logLik: -418.91 diff: 1.1e-08
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2112 iterations logLik: -418.91 diff: 1.1e-08
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#> .. 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: -418.9054
# Parameter restriction
mf <- estimate(m, dt$response)
param(mf, index = TRUE)
#> PI :
#> (lc)
#> class
#> 1 2 3
#> 0.2611 (1) 0.3788 (2) 0.3601 (3)
#>
#> RHO :
#> (a)
#> class
#> response 1 2 3
#> 1(V1) 0.8040 (4) 0.0330 (12) 0.8679 (20)
#> 2 0.1960 (5) 0.9670 (13) 0.1321 (21)
#> 1(V2) 0.8522 (6) 0.0000 (14) 0.9233 (22)
#> 2 0.1478 (7) 1.0000 (15) 0.0767 (23)
#> 1(V3) 0.0896 (8) 0.1054 (16) 0.8101 (24)
#> 2 0.9104 (9) 0.8946 (17) 0.1899 (25)
#> 1(V4) 0.0000 (10) 0.0802 (18) 0.8738 (26)
#> 2 1.0000 (11) 0.9198 (19) 0.1262 (27)
#>
#> V1 V2 V3 V4
#> lc y1 y2 y3 y4
mf0 <- estimate(mf, fix2zero = c(4, 6, 8, 10))
param(mf0)
#> PI :
#> (lc)
#> class
#> 1 2 3
#> 0.0000 0.4474 0.5526
#>
#> RHO :
#> (a)
#> class
#> response 1 2 3
#> 1(V1) 0.0000 0.0968 0.8898
#> 2 1.0000 0.9032 0.1102
#> 1(V2) 0.0000 0.0856 0.9351
#> 2 1.0000 0.9144 0.0649
#> 1(V3) 0.0000 0.0970 0.5638
#> 2 1.0000 0.9030 0.4362
#> 1(V4) 0.0000 0.0711 0.5667
#> 2 1.0000 0.9289 0.4333
#>
#> V1 V2 V3 V4
#> lc y1 y2 y3 y4
# Estimation control
estimate(m, dt$response, control = slcaControl(nrep = 3, verbose = TRUE))
#> Inital parameter test:
#> 1 / 3 logLik: -418.9081
#> 2 / 3 logLik: -418.9064
#> 3 / 3 logLik: -418.9062
#>
#> 3th parameter set has been selected.
#>
#> EM iteration begin.
#> 1 iterations logLik: -418.91 diff: inf
2 iterations logLik: -418.91 diff: 6.2e-06
3 iterations logLik: -418.91 diff: 6.2e-06
4 iterations logLik: -418.91 diff: 6.1e-06
5 iterations logLik: -418.91 diff: 6.1e-06
6 iterations logLik: -418.91 diff: 6.0e-06
7 iterations logLik: -418.91 diff: 5.9e-06
8 iterations logLik: -418.91 diff: 5.9e-06
9 iterations logLik: -418.91 diff: 5.8e-06
10 iterations logLik: -418.91 diff: 5.7e-06
11 iterations logLik: -418.91 diff: 5.7e-06
12 iterations logLik: -418.91 diff: 5.6e-06
13 iterations logLik: -418.91 diff: 5.6e-06
14 iterations logLik: -418.91 diff: 5.5e-06
15 iterations logLik: -418.91 diff: 5.5e-06
16 iterations logLik: -418.91 diff: 5.4e-06
17 iterations logLik: -418.91 diff: 5.4e-06
18 iterations logLik: -418.91 diff: 5.3e-06
19 iterations logLik: -418.91 diff: 5.2e-06
20 iterations logLik: -418.91 diff: 5.2e-06
21 iterations logLik: -418.91 diff: 5.1e-06
22 iterations logLik: -418.91 diff: 5.1e-06
23 iterations logLik: -418.91 diff: 5.0e-06
24 iterations logLik: -418.91 diff: 5.0e-06
25 iterations logLik: -418.91 diff: 4.9e-06
26 iterations logLik: -418.91 diff: 4.9e-06
27 iterations logLik: -418.91 diff: 4.8e-06
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31 iterations logLik: -418.91 diff: 4.6e-06
32 iterations logLik: -418.91 diff: 4.6e-06
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#> .. done.
#> Structural Latent Variable Model
#>
#> Latent variables (Root*):
#> Label: lc*
#> nclass: 3
#>
#> Measurement model:
#> lc -> { y1, y2, y3, y4 } a
#>
#> LogLik: -418.9054
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: -418.7988
