BM {DIMORA}

Standard Bass model

Description

Function that estimates the standard Bass model. Fitted values for cumulative and instantaneous data are displayed (if display = T). Out-of-sample prediction is performed based on estimated parameters.

Usage

BM(series, method = "nls", prelimestimates = c(sum(series) + 100, 0.01, 0.1),
   oos = round(length(series)*0.25), alpha = 0.05 ,display = T)

Arguments

series

the instantaneous observed data.

method

the estimation method, 'nlm' or 'optim' (see Details).

prelimestimates

a vector containing the starting values used by the algorithm to estimate the parameters. If no values are specified, the default ones are:

• market potential: m = \sum_{t}(series)+100;

• innovation coefficient: p = 0.01;

• imitation coefficient: q = 0.1.

alpha

the significance level for the confidence intervals.

oos

positive integer value: number of predictions after the last observed one. Default setting to 25% of the length of the data.

display

if TRUE returns the fitted values for cumulative and instantaneous observed data. If 'oos' is specified, it also returns the predicted fit values.

Details

The optim method provides only the parameter estimates. It does not provide the standard error and the p-value estimates.

Value

BM returns an object of class "Dimora".

The function summary is used to obtain and print a summary table of the results. The generic accessor functions coefficients, fitted and residuals extract various useful features of the value returned by BM.

An object of class "Dimora" is a list containing at least the following components:

model

the model formula used.

type

the model frame used.

Estimate

a summary table of estimates.

coefficients

a named vector of coefficients.

Rsquared

the statistical measure R-squared.

RSS

the residual sum of squares.

residuals

the residuals (observed cumulative data - fitted cumulative data).

fitted

the cumulative fitted values.

data

the cumulative observed series.

call

the matched call.

Author(s)

• Zanghi Federico: [e-mail]

  • https://www.linkedin.com/in/federico-zanghi-75512b165/

  • https://github.com/federicozanghi

• Savio Andrea: [e-mail]

  • https://www.linkedin.com/in/andrea-savio-51861b191/

• Ziliotto Filippo: [e-mail]

  • https://www.linkedin.com/in/FilippoZiliottoDev/

• Bessi Alessandro: [e-mail]

  • https://www.linkedin.com/in/alessandro-bessi-419812194/

References

Guidolin, M. (2023). Innovation Diffusion Models: Theory and Practice, First Edition. John Wiley & Sons Ltd.

Bass, F.M. (1969). A new product growth for model consumer durables. Management science, 15 (5), 215-227.

See Also

The Dimora models: GBM, GGM, UCRCD.

summary.Dimora for summaries.

plot.Dimora for graphics and residuals analysis.

predict.Dimora for prediction.

make.instantaneous to create instantaneous series from the cumulative one.

Examples

data(DBdimora)
iphone <- DBdimora$iPhone[7:52]

## Example 1
M1 <- BM(iphone)
summary(M1)
plot.Dimora(M1)
plot.Dimora(M1, oos=25)
# 25 predictions


## Example 2
M2 <- BM(iphone, prelimestimates = c(2000, 0.001, 0.1), method = "optim", oos = 100)
summary(M2)