Enumerate numbers of individual profiles and group classes

Fits every requested combination and retains errors and warnings alongside successful fits. Information criteria are descriptive: neither the smallest BIC nor high entropy guarantees the correct number of classes. Unconverged, boundary, and unreplicated fits are reported, not silently selected.

Usage

enumerate_classes(
  data,
  vars,
  id,
  n_profiles = 1:4,
  n_group_classes = 1:3,
  model = "basic",
  seed = NULL,
  family = "profiles",
  between_variance = c("varying", "equal"),
  time = NULL,
  ...
)

Arguments

data: Data frame.
vars: Continuous indicator names.
id: The column that identifies the groups the observations are nested in (students in schools, reports in students). NULL enumerates single-level models, with a message; enumerate_lpa() and enumerate_lca() fit those by name.
n_profiles: Positive integer profile counts to try.
n_group_classes: Positive integer group-class counts to try. With id = NULL it is 1 and may be left out.
model: The covariance structures to cross with the class counts. "basic", the default, fits the four structures that combine variances equal or varying across profiles with covariances absent or present: "EEI" (equal variances, no covariances), "VVI" (varying variances, no covariances), "EEE" (one covariance matrix shared by all profiles) and "VVV" (a covariance matrix for each profile). They are the choices that matter most in practice, since omitting covariances between correlated indicators makes the grid favour additional profiles. "all" fits all 14 structures of Celeux and Govaert (1995). Otherwise name the structures by their three-letter codes, as multilpa()'s model takes them: the letters give the volume, shape and orientation of each profile's covariance matrix, each equal (E) or varying (V) across profiles, with I for no covariances. NULL crosses no structures and fits whatever the other arguments ask for. With one continuous indicator the structures reduce to equal or varying variance, and codes that coincide are fitted once; with only categorical indicators there is no structure to cross. A structure set through variance_model, covariance_model, volume, shape or orientation replaces the default.
seed: Optional reproducible seed for each fit.
family: "profiles" (the default) enumerates the profile model over n_profiles, n_group_classes and model. One or more of the group-class families "additive", "dispersion" and "additive_dispersion" enumerates those instead, over family, n_group_classes and between_variance; n_profiles and model are then refused, and the result is a latents_family_enumeration read with get_results.latents_family_enumeration() and candidate_fit().
between_variance: For group-class families: the between-variance restrictions to cross, "varying", "equal" or both (the default). The dispersion family is always fitted with "equal".
time: The occasion column: enumerate latent transition models (lta()) over n_profiles (default 2:4) and n_group_classes (default 1), holding every other lta() argument given in ... fixed. model, when given, crosses those covariance structures. The result is a latents_transition_enumeration, read with get_results.latents_transition_enumeration() and candidate_fit().
...: Further arguments to multilpa() (or to lta() with time); for group-class families only n_starts, max_iter, tol and min_variance.

Value

An object of class multilpa_enumeration. Read it with the verbs that describe it rather than by reaching into it: as.data.frame() gives one row per candidate model with every criterion and diagnostic, summary() gives one row per information criterion naming the candidate that minimises it, plot() draws one criterion across the grid, and candidate_fit() returns the fitted model for one cell of the grid.

Conditions

latents_bad_argument when model names an unknown structure, when it is given together with another way of setting the structure, or when it is given although every indicator is categorical.

References

Celeux, G., & Govaert, G. (1995). Gaussian parsimonious clustering models. Pattern Recognition, 28(5), 781–793.

Examples

set.seed(1)
d <- data.frame(g = rep(1:10, each = 10), y = rnorm(100))
candidates <- enumerate_classes(d, "y", "g", n_profiles = 1:2,
                              n_group_classes = 1, n_starts = 2, seed = 1)
as.data.frame(candidates)
#>   n_profiles n_group_classes model log_likelihood n_parameters      aic
#> 1          1               1   EEI      -130.6550            2 265.3100
#> 2          2               1   EEI      -130.5791            4 269.1581
#> 3          1               1   VVI      -130.6550            2 265.3100
#> 4          2               1   VVI      -130.5920            5 271.1839
#>        kic bic_groups bic_individual sabic_groups sabic_individual caic_groups
#> 1 270.3100   265.9152       270.5204     259.9237         264.2039    267.9152
#> 2 276.1581   270.3684       279.5788     258.3855         266.9458    274.3684
#> 3 270.3100   265.9152       270.5204     259.9237         264.2039    267.9152
#> 4 279.1839   272.6968       284.2098     257.7182         268.4185    277.6968
#>   caic_individual awe_groups awe_individual icl_groups icl_individual
#> 1        272.5204   276.5204       285.7307   265.9152       270.5204
#> 2        283.5788   291.5788       386.0639   270.3684       355.6432
#> 3        272.5204   276.5204       285.7307   265.9152       270.5204
#> 4        289.2098   299.2098       449.6156   272.6968       411.5897
#>   clc_groups clc_individual profile_entropy group_entropy converged boundary
#> 1   261.3100       261.3100              NA            NA      TRUE    FALSE
#> 2   261.1581       337.2225      0.45131114            NA      TRUE    FALSE
#> 3   261.3100       261.3100              NA            NA      TRUE    FALSE
#> 4   261.1839       388.5639      0.08114782            NA      TRUE    FALSE
#>   n_best_replicated warnings error
#> 1                 2           <NA>
#> 2                 2           <NA>
#> 3                 2           <NA>
#> 4                 2           <NA>
summary(candidates)
#> Class enumeration: 4 candidates, 4 converged, 0 failed to fit
#> 3 distinct candidate(s) are minimal under some criterion.
#> No candidate is selected automatically. Choose one convention and keep it.
#> The candidates table shows 11 of its 26 columns; get_results(x, what = "candidates") returns all of them.
#> 
#> -- candidates ------------------------------------------------------
#>  n_profiles model log_likelihood n_parameters   aic bic_groups bic_individual
#>           1   EEI         -130.7            2 265.3      265.9          270.5
#>           2   EEI         -130.6            4 269.2      270.4          279.6
#>           1   VVI         -130.7            2 265.3      265.9          270.5
#>           2   VVI         -130.6            5 271.2      272.7          284.2
#>  icl_individual profile_entropy converged boundary
#>           270.5              NA      TRUE    FALSE
#>           355.6         0.45131      TRUE    FALSE
#>           270.5              NA      TRUE    FALSE
#>           411.6         0.08115      TRUE    FALSE
#> 
#> -- criteria --------------------------------------------------------
#>  criterion  convention n_profiles n_group_classes model value
#>        aic        <NA>          1               1   EEI 265.3
#>        kic        <NA>          1               1   EEI 270.3
#>        bic      groups          1               1   EEI 265.9
#>        bic individuals          1               1   EEI 270.5
#>      sabic      groups          2               1   VVI 257.7
#>      sabic individuals          1               1   EEI 264.2
#>       caic      groups          1               1   EEI 267.9
#>       caic individuals          1               1   EEI 272.5
#>        awe      groups          1               1   EEI 276.5
#>        awe individuals          1               1   EEI 285.7
#>    ... 4 more rows.  get_results(x, what = "criteria")
#> 
#> 2 tables above, truncated to fit. get_results(x, what = ) returns any
#> of them whole, and get_results(x, what = "all") returns every one.

# Single level, crossing class counts with two named structures:
single <- enumerate_lpa(iris, c("Sepal.Length", "Sepal.Width",
                                "Petal.Length", "Petal.Width"),
                        n_profiles = 1:3, model = c("VVV", "EEE"),
                        n_starts = 2, seed = 1)
summary(single)
#> Class enumeration: 6 candidates, 6 converged, 0 failed to fit
#> 2 distinct candidate(s) are minimal under some criterion.
#> No candidate is selected automatically. Choose one convention and keep it.
#> The candidates table shows 10 of its 26 columns; get_results(x, what = "candidates") returns all of them.
#> 
#> -- candidates ------------------------------------------------------
#>  n_profiles model log_likelihood n_parameters   aic   bic icl_individual
#>           1   VVV         -379.9           14 787.8 830.0          830.0
#>           2   VVV         -214.4           29 486.7 574.0          574.0
#>           3   VVV         -180.2           44 448.4 580.8          590.6
#>           1   EEE         -379.9           14 787.8 830.0          830.0
#>           2   EEE         -296.4           19 630.9 688.1          688.1
#>           3   EEE         -256.4           24 560.7 633.0          645.6
#>  profile_entropy converged boundary
#>               NA      TRUE    FALSE
#>           0.9999      TRUE    FALSE
#>           0.9704      TRUE    FALSE
#>               NA      TRUE    FALSE
#>           0.9999      TRUE    FALSE
#>           0.9616      TRUE    FALSE
#> 
#> -- criteria --------------------------------------------------------
#>  criterion  convention n_profiles n_group_classes model value
#>        aic        <NA>          3               1   VVV 448.4
#>        kic        <NA>          3               1   VVV 495.4
#>        bic      groups          2               1   VVV 574.0
#>        bic individuals          2               1   VVV 574.0
#>      sabic      groups          3               1   VVV 441.6
#>      sabic individuals          3               1   VVV 441.6
#>       caic      groups          2               1   VVV 603.0
#>       caic individuals          2               1   VVV 603.0
#>        awe      groups          2               1   VVV 806.3
#>        awe individuals          2               1   VVV 806.3
#>    ... 4 more rows.  get_results(x, what = "criteria")
#> 
#> 2 tables above, truncated to fit. get_results(x, what = ) returns any
#> of them whole, and get_results(x, what = "all") returns every one.