The class `estimate.mpin.ecm`

is the blueprint of
`S4`

objects that store the results of the estimation of the `MPIN`

model using the Expectation-Conditional Maximization method, as
implemented in the function `mpin_ecm()`

.

## Usage

```
# S4 method for estimate.mpin.ecm
show(object)
selectModel(object, criterion)
# S4 method for estimate.mpin.ecm
selectModel(object, criterion)
getSummary(object)
# S4 method for estimate.mpin.ecm
getSummary(object)
```

## Arguments

- object
an object of class

`estimate.mpin.ecm`

.- criterion
a character string specifying the model selection criterion.

`criterion`

should take one of these values`{"BIC", "AIC", "AWE"}`

. They stand for Bayesian Information Criterion, Akaike Information Criterion, and Approximate Weight of Evidence, respectively.

## Functions

`selectModel,estimate.mpin.ecm-method`

: returns the optimal model among the estimated models, i.e., the model having the lowest information criterion, provided by the user.`getSummary,estimate.mpin.ecm-method`

: returns a summary of the estimation of the`MPIN`

model using the`ECM`

algorithm for different values of the argument`layers`

. For each estimation, the number of layers, the`MPIN`

value, the log-likelihood value, as well as the values of the different information criteria, namely`AIC`

,`BIC`

and`AWE`

are displayed.

## Slots

`success`

(

`logical`

) returns the value`TRUE`

when the estimation has succeeded,`FALSE`

otherwise.`errorMessage`

(

`character`

) returns an error message if the`MPIN`

estimation has failed, and is empty otherwise.`convergent.sets`

(

`numeric`

) returns the number of initial parameter sets at which the likelihood maximization converged.`method`

(

`character`

) returns the method of estimation, and is equal to 'Expectation-Conditional Maximization Algorithm'.`layers`

(

`numeric`

) returns the number of layers estimated by the Expectation-Conditional Maximization algorithm, or provided by the user.`optimal`

(

`logical`

) returns whether the number of layers used for the estimation is provided by the user`(optimal=FALSE)`

, or determined by the`ECM`

algorithm`(optimal=TRUE)`

.`parameters`

(

`list`

) returns the list of the maximum likelihood estimates (\(\alpha\), \(\delta\), \(\mu\), \(\epsilon\)_{b}, \(\epsilon\)_{s}), where \(\alpha\), \(\delta\), and \(\mu\) are numeric vectors of length`layers`

.`aggregates`

(

`numeric`

) returns an aggregation of information layers' parameters alongside with \(\epsilon\)_{b}and \(\epsilon\)_{s}. The aggregated parameters are calculated as follows: \(\alpha_{agg} = \sum \alpha_j\)\(\alpha*= \sum \alpha\)_{j}\(\delta_{agg} = \sum \alpha_j \times \delta_j\) \(\delta*= \sum \alpha\)_{j}\(\delta\)_{j}, and \(\mu_{agg} = \sum \alpha_j \times \mu_j\)\(\mu*= \sum \alpha\)_{j}\(\mu\)_{j}.`likelihood`

(

`numeric`

) returns the value of the (log-)likelihood function evaluated at the optimal set of parameters.`mpinJ`

(

`numeric`

) returns the values of the multilayer probability of informed trading per layer, calculated using the layer-specific estimated parameters.`mpin`

(

`numeric`

) returns the global value of the multilayer probability of informed trading. It is the sum of the multilayer probabilities of informed trading per layer stored in the slot`mpinJ`

.`mpin.goodbad`

(

`list`

) returns a list containing a decomposition of`MPIN`

into good-news, and bad-news`MPIN`

components. The decomposition has been suggested for PIN measure in Brennan et al. (2016) . The list has four elements:`mpinG`

, and`mpinB`

are the global good-news, and bad-news components of`MPIN`

, while`mpinGj`

, and`mpinBj`

are two vectors containing the good-news (bad-news) components of`MPIN`

computed per layer.`dataset`

(

`dataframe`

) returns the dataset of buys and sells used in the ECM estimation of the MPIN model.`initialsets`

(

`dataframe`

) returns the initial parameter sets used in the ECM estimation of the MPIN model.`details`

(

`dataframe`

) returns a dataframe containing the estimated parameters of the`ECM`

method for each initial parameter set.`models`

(

`list`

) returns the list of`estimate.mpin.ecm`

objects storing the results of estimation using the function`mpin_ecm()`

for different values of the argument`layers`

. It returns`NULL`

when the argument`layers`

of the function`mpin_ecm()`

take a specific value.`AIC`

(

`numeric`

) returns the value of the Akaike Information Criterion (AIC).`BIC`

(

`numeric`

) returns the value of the Bayesian Information Criterion (BIC).`AWE`

(

`numeric`

) returns the value of the Approximate Weight of Evidence.`criterion`

(

`character`

) returns the model selection criterion used to find the optimal estimate for the`MPIN`

model. It takes one of these values`'BIC'`

,`'AIC'`

,`'AWE'`

; which stand for Bayesian Information Criterion, Akaike Information Criterion, and Approximate Weight of Evidence, respectively.`hyperparams`

(

`list`

) returns the hyperparameters of the`ECM`

algorithm, which are`minalpha`

,`maxeval`

,`tolerance`

, and`maxlayers`

. Check the details section of`mpin_ecm()`

to know more about these parameters.`runningtime`

(

`numeric`

) returns the running time of the estimation in seconds.