# bgbb.rf.matrix.PosteriorMeanDropoutRate: BG/BB Posterior Mean Dropout Rate using a recency-frequency... In BTYD: Implementing BTYD Models with the Log Sum Exp Patch

## Description

Computes the mean value of the marginal posterior value of Theta, the geometric dropout process parameter.

## Usage

 `1` ```bgbb.rf.matrix.PosteriorMeanDropoutRate(params, rf.matrix) ```

## Arguments

 `params` BG/BB parameters - a vector with alpha, beta, gamma, and delta, in that order. Alpha and beta are unobserved parameters for the beta-Bernoulli transaction process. Gamma and delta are unobserved parameters for the beta-geometric dropout process. `rf.matrix` recency-frequency matrix. It must contain columns for frequency ("x"), recency ("t.x"), number of transaction opportunities in the calibration period ("n.cal"), and the number of customers with this combination of recency, frequency and transaction opportunities in the calibration period ("custs"). Note that recency must be the time between the start of the calibration period and the customer's last transaction, not the time between the customer's last transaction and the end of the calibration period.

## Details

E(Theta | alpha, beta, gamma, delta, x, t.x, n). This is calculated by setting `l = 0` and `m = 1` in `bgbb.PosteriorMeanLmProductMoment`.

`rf.matrix` has columns x`, `t.x`, and `n.cal'.

## Value

The posterior mean dropout rate.

## References

Fader, Peter S., Bruce G.S. Hardie, and Jen Shang. "Customer-Base Analysis in a Discrete-Time Noncontractual Setting." Marketing Science 29(6), pp. 1086-1108. 2010. INFORMS. Web.

`bgbb.PosteriorMeanDropoutRate`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```data(donationsSummary) rf.matrix <- donationsSummary\$rf.matrix # donationsSummary\$rf.matrix already has appropriate column names # starting-point parameters startingparams <- c(1, 1, 0.5, 3) # estimated parameters est.params <- bgbb.EstimateParameters(rf.matrix, startingparams) # return the posterior mean dropout rate vector bgbb.rf.matrix.PosteriorMeanDropoutRate(est.params, rf.matrix) ```

### Example output

```Loading required package: hypergeo
[1] 0.06955854 0.06955854 0.06955854 0.06955854 0.06955854 0.06955854
[7] 0.11606209 0.09615814 0.08818559 0.08389008 0.08120446 0.16752458
[13] 0.13431763 0.11391216 0.10173828 0.20358250 0.16754421 0.13711654
[19] 0.23732732 0.19368820 0.27432512 0.31036693
```

BTYD documentation built on Nov. 18, 2021, 1:10 a.m.