Calculates the Log-Likelihood values for the Pareto/NBD model with and without covariates.

The function `pnbd_nocov_LL_ind`

calculates the individual LogLikelihood
values for each customer for the given parameters.

The function `pnbd_nocov_LL_sum`

calculates the LogLikelihood value summed
across customers for the given parameters.

The function `pnbd_staticcov_LL_ind`

calculates the individual LogLikelihood
values for each customer for the given parameters and covariates.

The function `pnbd_staticcov_LL_sum`

calculates the individual LogLikelihood values summed
across customers.

pnbd_nocov_LL_ind(vLogparams, vX, vT_x, vT_cal) pnbd_nocov_LL_sum(vLogparams, vX, vT_x, vT_cal) pnbd_staticcov_LL_ind(vParams, vX, vT_x, vT_cal, mCov_life, mCov_trans) pnbd_staticcov_LL_sum(vParams, vX, vT_x, vT_cal, mCov_life, mCov_trans)

vLogparams | vector with the Pareto/NBD model parameters at log scale. See Details. |
---|---|

vX | Frequency vector of length n counting the numbers of purchases. |

vT_x | Recency vector of length n. |

vT_cal | Vector of length n indicating the total number of periods of observation. |

vParams | vector with the parameters for the Pareto/NBD model at log scale and the static covariates at original scale. See Details. |

mCov_life | Matrix containing the covariates data affecting the lifetime process. One column for each covariate. |

mCov_trans | Matrix containing the covariates data affecting the transaction process. One column for each covariate. |

Returns the respective Log-Likelihood value(s) for the Pareto/NBD model with or without covariates.

`vLogparams`

is a vector with model parameters `r, alpha_0, s, beta_0`

at log-scale, in this order.

`vParams`

is vector with the Pareto/NBD model parameters at log scale,
followed by the parameters for the lifetime covariates at original scale and then
followed by the parameters for the transaction covariates at original scale

`mCov_trans`

is a matrix containing the covariates data of
the time-invariant covariates that affect the transaction process.
Each column represents a different covariate. For every column a gamma parameter
needs to added to `vParams`

at the respective position.

`mCov_life`

is a matrix containing the covariates data of
the time-invariant covariates that affect the lifetime process.
Each column represents a different covariate. For every column a gamma parameter
needs to added to `vParams`

at the respective position.

Schmittlein DC, Morrison DG, Colombo R (1987). “Counting Your Customers: Who-Are They and What Will They Do Next?” Management Science, 33(1), 1–24.

Fader PS, Hardie BGS (2005). “A Note on Deriving the Pareto/NBD Model and Related Expressions.” URL http://www.brucehardie.com/notes/009/pareto_nbd_derivations_2005-11-05.pdf.

Fader PS, Hardie BG (2007). “Incorporating time-invariant covariates into the Pareto/NBD and BG/NBD models.” URL http://www.brucehardie.com/notes/019/time_invariant_covariates.pdf.