psm_analysis_weighted: Weighted van Westendorp Price Sensitivity Meter Analysis...
In pricesensitivitymeter: Van Westendorp Price Sensitivity Meter Analysis

Description Usage Arguments Details Value References Examples

psm_analysis_weighted() performs a weighted analysis of consumer price preferences and price sensitivity known as van Westendorp Price Sensitivity Meter (PSM). The function requires a sample design from the survey package as the main input. Custom weights or sample designs from other packages are not supported.

To run a PSM analysis without weighting, use the function psm_analysis.

psm_analysis_weighted(
  toocheap, cheap, expensive, tooexpensive,
  design,
  validate = TRUE,
  interpolate = FALSE,
  interpolation_steps = 0.01,
  intersection_method = "min",
  pi_cheap = NA, pi_expensive = NA,
  pi_scale = 5:1,
  pi_calibrated = c(0.7, 0.5, 0.3, 0.1, 0))

`toocheap, cheap, expensive, tooexpensive`	Names of the variables in the data.frame/matrix that contain the survey data on the respondents' "too cheap", "cheap", "expensive" and "too expensive" price preferences. If the `toocheap` price was not assessed, a variable of NAs can be used instead. If `toocheap` is NA for all cases, it is possible to calculate the Point of Marginal Expensiveness and the Indifference Price Point, but it is impossible to calculate the Point of Marginal Cheapness and the Optimal Price Point.
`design`	A survey design which has been created by the function `svydesign()` from the survey package. The data that is used as an input of `svydesign()` must include all the variable names for `toocheap`, `cheap`, `expensive` and `tooexpensive` variables specified above.
`validate`	logical. should only respondents with consistent price preferences (too cheap < cheap < expensive < too expensive) be considered in the analysis?
`interpolate`	logical. should interpolation of the price curves be applied between the actual prices given by the respondents? If interpolation is enabled, the output appears less bumpy in regions with sparse price information. If the sample size is sufficiently large, interpolation should not be necessary.
`interpolation_steps`	numeric. if `interpolate` is `TRUE`: the size of the interpolation steps. Set by default to 0.01, which should be appropriate for most goods in a price range of 0-50 USD/Euro.
`intersection_method`	"min" (default), "max", "mean" or "median". defines the method how to determine the price points (range, indifference price, optimal price) if there are multiple possible intersections of the price curves. "min" uses the lowest possible prices, "max" uses the highest possible prices, "mean" calculates the mean among all intersections and "median" uses the median of all possible intersections
`pi_cheap, pi_expensive`	Only required for the Newton Miller Smith extension. Names of the variables in the data that contain the survey data on the respondents' purchase intent at their individual cheap/expensive price.
`pi_scale`	Only required for the Newton Miller Smith extension. Scale of the purchase intent variables pi_cheap and pi_expensive. By default assuming a five-point scale with 5 indicating the highest purchase intent.
`pi_calibrated`	Only required for the Newton Miller Smith extension. Calibrated purchase probabilities that are assumed for each value of the purchase intent scale. Must be the same order as the pi_scale variable so that the first value of pi_calibrated corresponds to the first value in the pi_scale variable. Default values are taken from the Sawtooth Software PSM implementation in Excel: 70% for the best value of the purchase intent scale, 50% for the second best value, 30% for the third best value (middle of the scale), 10% for the fourth best value and 0% for the worst value.

The main logic of the Price Sensitivity Meter Analysis is explained in the documentation of the psm_analysis function. The psm_analysis_weighted performs the same analysis, but weights the survey data according to a known population.

The function output consists of the following elements:

`data_input:`	`data.frame` object. Contains the data that was used as an input for the analysis.
`validated:`	`logical` object. Indicates whether the `"validate"` option has been used (to exclude cases with intransitive price preferences).
`invalid_cases:`	`numeric` object. Number of cases with intransitive price preferences.
`total_sample:`	`"numeric"` object. Total sample size of the input sample before assessing the transitivity of individual price preferences.
`data_vanwestendorp:`	`data.frame` object. Output data of the Price Sensitivity Meter analysis. Contains the weighted cumulative distribution functions for the four price assessments (too cheap, cheap, expensive, too expensive) for all prices.
`pricerange_lower:`	`numeric` object. Lower limit of the acceptable price range as defined by the Price Sensitivity Meter, also known as point of marginal cheapness: Intersection of the "too cheap" and the "expensive" curves.
`pricerange_upper:`	`numeric` object. Upper limit of the acceptable price range as defined by the Price Sensitivity Meter, also known as point of marginal expensiveness: Intersection of the "too expensive" and the "cheap" curves.
`idp:`	`numeric` object. Indifference Price Point as defined by the Price Sensitivity Meter: Intersection of the "cheap" and the "expensive" curves.
`opp:`	`numeric` object. Optimal Price Point as defined by the Price Sensitivity Meter: Intersection of the "too cheap" and the "too expensive" curves.
`weighted:`	`logical` object. Indicating if weighted data was used in the analysis. Outputs from `psm_analysis_weighted()` always have the value `TRUE`. When data is unweighted, use the function `psm_analysis.`
`survey_design:`	`survey.design2` object. Returning the full survey design as specified with the `svydesign` function from the survey package.
`NMS:`	`logical` object. Indicates whether the additional analyses of the Newton Miller Smith Extension were performed.

Van Westendorp, P (1976) "NSS-Price Sensitivity Meter (PSM) – A new approach to study consumer perception of price" Proceedings of the ESOMAR 29th Congress, 139–167. Online available at https://www.researchworld.com/a-new-approach-to-study-consumer-perception-of-price/.

Newton, D, Miller, J, Smith, P, (1993) "A market acceptance extension to traditional price sensitivity measurement" Proceedings of the American Marketing Association Advanced Research Techniques Forum.

Sawtooth Software (2016) "Templates for van Westendorp PSM for Lighthouse Studio and Excel". Online available at https://sawtoothsoftware.com/resources/software-downloads/tools/van-westendorp-price-sensitivity-meter

# assuming a skewed sample with only 1/3 women and 2/3 men

input_data <- data.frame(tch = round(rnorm(n = 250, mean = 8, sd = 1.5), digits = 2),
                         ch = round(rnorm(n = 250, mean = 12, sd = 2), digits = 2),
                         ex = round(rnorm(n = 250, mean = 13, sd = 1), digits = 2),
                         tex = round(rnorm(n = 250, mean = 15, sd = 1), digits = 2),
                         gender = sample(x = c("male", "female"),
                                         size = 250,
                                         replace = TRUE,
                                         prob = c(2/3, 1/3)))

# ... and in which women have on average 1.5x the price acceptance of men
input_data$tch[input_data$gender == "female"] <- input_data$tch[input_data$gender == "female"] * 1.5
input_data$ch[input_data$gender == "female"] <- input_data$ch[input_data$gender == "female"] * 1.5
input_data$ex[input_data$gender == "female"] <- input_data$ex[input_data$gender == "female"] * 1.5
input_data$tex[input_data$gender == "female"] <- input_data$tex[input_data$gender == "female"] * 1.5

# creating a sample design object using the survey package
# ... assuming that gender is balanced equally in the population of 10000

input_data$gender_pop <- 5000

input_design <- survey::svydesign(ids = ~ 1, # no clusters
                          probs = NULL, # hence no cluster samling probabilities,
                          strata = input_data$gender, # stratified by gender
                          fpc = input_data$gender_pop, # strata size in the population
                          data = input_data)
                          # data object used as input: no need to specify single variables


output_weighted_psm <- psm_analysis_weighted(toocheap = "tch",
  cheap = "ch",
  expensive = "ex",
  tooexpensive = "tex",
  design = input_design)

summary(output_weighted_psm)