psm_analysis_weighted {pricesensitivitymeter}

Weighted van Westendorp Price Sensitivity Meter Analysis (PSM)

Description

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.

Usage

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

Arguments

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

acceptable_range

"original" (default) or "narrower". Defines which intersection is used to calculate the point of marginal cheapness and point of marginal expensiveness, which together form the range of acceptable prices. "original" uses the definition provided in van Westendorp's paper: The lower end of the price range (point of marginal cheapness) is defined as the intersection of "too cheap" and the inverse of the "cheap" curve. The upper end of the price range (point of marginal expensiveness) is defined as the intersection of "too expensive" and the inverse of the "expensive" curve. Alternatively, it is possible to use a "narrower" definition which is applied by some market research companies. Here, the lower end of the price range is defined as the intersection of the "expensive" and the "too cheap" curves and the upper end of the price range is defined as the intersection of the "too expensive" and the "cheap" curves. This leads to a narrower range of acceptable prices. Note that it is possible that the optimal price according to the Newton/Miller/Smith extension is higher than the upper end of the acceptable price range in the "narrower" definition.

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.

pi_calibrated_toocheap, pi_calibrated_tooexpensive

Only required for the Newton Miller Smith extension. Calibrated purchase probabilities for the "too cheap" and the "too expensive" price, respectively. Must be a value between 0 and 1; by default set to zero following the logic in van Westendorp's paper.

Details

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.

Value

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.

References

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://archive.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

Examples

# 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)