Compute internal model metric(s)

Compute one or more internal metrics for the given lcModel object.

Note that there are many metrics available, and there exists no metric that works best in all scenarios. It is recommended to carefully consider which metric is most appropriate for your use case.

Recommended overview papers:

arbelaitz2013extensive;textuallatrend provide an extensive overview validity indices for cluster algorithms.
vandernest2020overview;textuallatrend provide an overview of metrics for mixture models (GBTM, GMM); primarily likelihood-based or posterior probability-based metrics.
henson2007detecting;textuallatrend provide an overview of likelihood-based metrics for mixture models.

Call getInternalMetricNames() to retrieve the names of the defined internal metrics.

See the Details section below for a list of supported metrics.

metric(object, name = getOption("latrend.metric", c("WRSS", "APPA.mean")), ...)

# S4 method for class 'lcModel'
metric(object, name = getOption("latrend.metric", c("WRSS", "APPA.mean")), ...)

# S4 method for class 'list'
metric(object, name, drop = TRUE)

# S4 method for class 'lcModels'
metric(object, name, drop = TRUE)

Arguments

object: The lcModel, lcModels, or list of lcModel objects to compute the metrics for.
name: The name(s) of the metric(s) to compute. If no names are given, the names specified in the latrend.metric option (WRSS, APPA, AIC, BIC) are used.
...: Additional arguments.
drop: Whether to return a numeric vector instead of a data.frame in case of a single metric.

Value

For metric(lcModel): A named numeric vector with the computed model metrics.

For metric(list): A data.frame with a metric per column.

For metric(lcModels): A data.frame with a metric per column.

Supported internal metrics

Metric name	Description	Function / Reference
`AIC`	Akaike information criterion. A goodness-of-fit estimator that adjusts for model complexity (i.e., the number of parameters). Only available for models that support the computation of the model log-likelihood through logLik.	`stats::AIC()`, akaike1974newlatrend
`APPA.mean`	Mean of the average posterior probability of assignment (APPA) across clusters. A measure of the precision of the trajectory classifications. A score of 1 indicates perfect classification.	`APPA()`, nagin2005grouplatrend
`APPA.min`	Lowest APPA among the clusters	`APPA()`, nagin2005grouplatrend
`ASW`	Average silhouette width based on the Euclidean distance	rousseeuw1987silhouetteslatrend
`BIC`	Bayesian information criterion. A goodness-of-fit estimator that corrects for the degrees of freedom (i.e., the number of parameters) and sample size. Only available for models that support the computation of the model log-likelihood through logLik.	`stats::BIC()`, schwarz1978estimatinglatrend
`CAIC`	Consistent Akaike information criterion	bozdogan1987modellatrend
`CLC`	Classification likelihood criterion	mclachlan2000finitelatrend
`converged`	Whether the model converged during estimation	`converged()`
`deviance`	The model deviance	`stats::deviance()`
`Dunn`	The Dunn index	dunn1974welllatrend
`entropy`	Entropy of the posterior probabilities
`estimationTime`	The time needed for fitting the model	`estimationTime()`
`ED`	Euclidean distance between the cluster trajectories and the assigned observed trajectories
`ED.fit`	Euclidean distance between the cluster trajectories and the assigned fitted trajectories
`ICL.BIC`	Integrated classification likelihood (ICL) approximated using the BIC	biernacki2000assessinglatrend
`logLik`	Model log-likelihood	`stats::logLik()`
`MAE`	Mean absolute error of the fitted trajectories (assigned to the most likely respective cluster) to the observed trajectories
`Mahalanobis`	Mahalanobis distance between the cluster trajectories and the assigned observed trajectories	mahalanobis1936generalizedlatrend
`MSE`	Mean squared error of the fitted trajectories (assigned to the most likely respective cluster) to the observed trajectories
`relativeEntropy`, `RE`	A measure of the precision of the trajectory classification. A value of 1 indicates perfect classification, whereas a value of 0 indicates a non-informative uniform classification. It is the normalized version of `entropy`, scaled between [0, 1].	ramaswamy1993empiricallatrend, muthen2004latentlatrend
`RMSE`	Root mean squared error of the fitted trajectories (assigned to the most likely respective cluster) to the observed trajectories
`RSS`	Residual sum of squares under most likely cluster allocation
`scaledEntropy`	See `relativeEntropy`
`sigma`	The residual standard deviation	`stats::sigma()`
`ssBIC`	Sample-size adjusted BIC	sclove1987applicationlatrend
`SED`	Standardized Euclidean distance between the cluster trajectories and the assigned observed trajectories
`SED.fit`	The cluster-weighted standardized Euclidean distance between the cluster trajectories and the assigned fitted trajectories
`WMAE`	`MAE` weighted by cluster-assignment probability
`WMSE`	`MSE` weighted by cluster-assignment probability
`WRMSE`	`RMSE` weighted by cluster-assignment probability
`WRSS`	`RSS` weighted by cluster-assignment probability

Implementation

See the documentation of the defineInternalMetric() function for details on how to define your own metrics.

References

Examples

data(latrendData)
method <- lcMethodLMKM(Y ~ Time, id = "Id", time = "Time")
model <- latrend(method, latrendData)
metric(model, "WMAE")
#>      WMAE 
#> 0.2158127 

if (require("clusterCrit")) {
  metric(model, c("WMAE", "Dunn"))
}
#>      WMAE      Dunn 
#> 0.2158127 0.2204919