Docu: Summary significance indicators NA

man-roxygen/template_examples_nocovmodelinterface.R

@@ -21,7 +21,10 @@
 #' # estimated coefs
 #' coef(apparel.<%=name_model_short%>)
 #'
-#' # summary of the fitted model
+#' # summary of the fitted model.
+#' # Note that the significance indicators are set to NA on purpose because all
+#' # model parameters are by definition strictly positive. A hypothesis test
+#' # relative to a null of 0 therefore does not make sense.
 #' summary(apparel.<%=name_model_short%>)
 #'
 #' # predict CLV etc for holdout period

man-roxygen/template_summary_clvfitted.R

@@ -14,6 +14,11 @@
 #' (for example if specified in parameter \code{optimx.args}), all information here refers to
 #' the last method/row of the resulting \code{optimx} object.
 #'
+#' Note that for the main model coefficients (all coefs not for covariates),
+#' the significance indicators \code{z-val} and p-values are set to \code{NA} because they are by definition always
+#' strictly positive and hypothesis test relative to a null of 0 does not make sense.
+#'
+#'
 #' @return This function computes and returns a list of summary information of the fitted model
 #' given in \code{object}. It returns a list of class \code{summary.clv.no.covariates} that contains the
 #' following components:

vignettes/CLVTools.Rmd

@@ -155,7 +155,7 @@ To execute the model estimation you have the choice between a formula-based inte
 
 
 
-Parameter estimates may be reported by either printing the estimated object (i.e. `est.pnbd`) directly in the console or by calling `summary(est.pnbd)` to get a more detailed report including the likelihood value as well as AIC and BIC. Alternatively parameters may be directly extracted using `coef(est.pnbd)`. Also `loglik()`, `confint()` and `vcov()` are available to directly access the Loglikelihood value, confidence intervals for the parameters and to calculate the Variance-Covariance Matrix for the fitted model. For the standard Pareto/NBD model, we get 4 parameters $r, \alpha, s$ and $\beta$.  where $r,\alpha$ represent the shape and scale parameter of the gamma distribution that determines the purchase rate and $s,\beta$ of the attrition rate across individual customers. $r/\alpha$ can be interpreted as the mean purchase and $s/\beta$ as the mean attrition rate. A significance level is provided for each parameter estimates. In the case of the apparelTrans dataset we observe a an average purchase rate of $r/\alpha=0.147$ transactions and an average attrition rate of $s/\beta=0.031$ per customer per week. KKT 1 and 2 indicate the Karush-Kuhn-Tucker optimality conditions of the first and second order [@KKT]. If those criteria are not met, the optimizer has probably not arrived at an optimal solution. If this is the case it is usually a good idea to rerun the estimation using alternative starting values.
+Parameter estimates may be reported by either printing the estimated object (i.e. `est.pnbd`) directly in the console or by calling `summary(est.pnbd)` to get a more detailed report including the likelihood value as well as AIC and BIC. Alternatively parameters may be directly extracted using `coef(est.pnbd)`. Also `loglik()`, `confint()` and `vcov()` are available to directly access the Loglikelihood value, confidence intervals for the parameters and to calculate the Variance-Covariance Matrix for the fitted model. For the standard Pareto/NBD model, we get 4 parameters $r, \alpha, s$ and $\beta$.  where $r,\alpha$ represent the shape and scale parameter of the gamma distribution that determines the purchase rate and $s,\beta$ of the attrition rate across individual customers. $r/\alpha$ can be interpreted as the mean purchase and $s/\beta$ as the mean attrition rate. Note that the significance indicators are set to `NA` for each parameter. The main model parameters are by definition always strictly positive and a hypothesis test relative to a null of 0 therefore does not make sense. In the case of the apparelTrans dataset we observe a an average purchase rate of $r/\alpha=0.147$ transactions and an average attrition rate of $s/\beta=0.031$ per customer per week. KKT 1 and 2 indicate the Karush-Kuhn-Tucker optimality conditions of the first and second order [@KKT]. If those criteria are not met, the optimizer has probably not arrived at an optimal solution. If this is the case it is usually a good idea to rerun the estimation using alternative starting values.
 
 
 ```{r param-summary}
@@ -383,7 +383,7 @@ est.pnbd.dyn <- pnbd(clv.dyn,
                      optimx.args = list(control=list(trace=5)))
 ```
 
-To inspect the estimated model we use `summary()`, however all other commands such as `print()`, `coef()`, `loglike()`, `confint()` and `vcov()` are also available. Now, output contains also parameters for the covariates for both processes. Since covariates are added separately for the purchase and the attrition process, there are also separate model parameters for the two processes. These parameters are directly interpretable as rate elasticity of the corresponding factors: A 1% change in a contextual factor $\bf{X}^{P}$ or $\bf{X}^{L}$ changes the purchase or the attrition rate by $\gamma_{purch}\bf{X}^{P}$ or $\gamma_{life}\bf{X}^{L}$ percent, respectively  [@Gupta1991]. In the example of the apparel retailer, we observe that female customer purchase significantly more (`trans.Gender=1.42576`). Note, that female customers are coded as 1, male customers as 0. Also customers acquired offline (coded as Channel=1), purchase more (`trans.Channel=0.40304`) and stay longer (`life.Channel=0.9343`). Make sure to check the Karush-Kuhn-Tucker optimality conditions of the first and second order [@KKT] (KKT1 and KKT1) before interpreting the parameters. If those criteria are not met, the optimizer has probably not arrived at an optimal solution. If this is the case it is usually a good idea to rerun the estimation using alternative starting values.
+To inspect the estimated model we use `summary()`, however all other commands such as `print()`, `coef()`, `loglike()`, `confint()` and `vcov()` are also available. Now, output contains also parameters for the covariates for both processes. Since covariates are added separately for the purchase and the attrition process, there are also separate model parameters for the two processes. Note that while significance indicators are `NA` for the main model parameters, they are present for the covariate parameters because a hypothesis test relative to a null of 0 does make sense for them. These parameters are directly interpretable as rate elasticity of the corresponding factors: A 1% change in a contextual factor $\bf{X}^{P}$ or $\bf{X}^{L}$ changes the purchase or the attrition rate by $\gamma_{purch}\bf{X}^{P}$ or $\gamma_{life}\bf{X}^{L}$ percent, respectively  [@Gupta1991]. In the example of the apparel retailer, we observe that female customer purchase significantly more (`trans.Gender=1.42576`). Note, that female customers are coded as 1, male customers as 0. Also customers acquired offline (coded as Channel=1), purchase more (`trans.Channel=0.40304`) and stay longer (`life.Channel=0.9343`). Make sure to check the Karush-Kuhn-Tucker optimality conditions of the first and second order [@KKT] (KKT1 and KKT1) before interpreting the parameters. If those criteria are not met, the optimizer has probably not arrived at an optimal solution. If this is the case it is usually a good idea to rerun the estimation using alternative starting values.
 
 
 ```{r Cov-summary}