psm_analysis_weighted.Rdpsm_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 = get_psm_constant("DEFAULT_INTERPOLATION_STEPS"),
intersection_method = "min",
acceptable_range = "original",
pi_cheap = NA, pi_expensive = NA,
pi_scale = get_psm_constant("NMS_DEFAULTS.PI_SCALE"),
pi_calibrated = get_psm_constant("NMS_DEFAULTS.PI_CALIBRATED"),
pi_calibrated_toocheap = get_psm_constant("NMS_DEFAULTS.PI_CALIBRATED_TOOCHEAP"),
pi_calibrated_tooexpensive = get_psm_constant("NMS_DEFAULTS.PI_CALIBRATED_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.
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.
logical. should only respondents with consistent price preferences (too cheap < cheap < expensive < too expensive) be considered in the analysis?
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.
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.
"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
"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.
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.
Only required for the Newton Miller Smith
extension. Scale of the purchase intent variables pi_cheap and
pi_expensive. By default using 5:1, assuming a
five-point scale with 5 indicating the highest purchase intent.
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 c(0.7, 0.5, 0.3, 0.1, 0,
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.
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 0 following the logic in van
Westendorp's paper.
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://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
# 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$gender_pop <- 5000
input_design <- survey::svydesign(ids = ~ 1, # no clusters
probs = NULL, # hence no cluster sampling probabilities,
strata = input_data$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)
#> Van Westendorp Price Sensitivity Meter Analysis
#>
#> Accepted Price Range: 11.38 - 16.79
#> Indifference Price Point: 14.02405
#> Optimal Price Point: 14.15909
#>
#> ---
#> 125 cases with individual price preferences were analyzed (weighted data).
#> Total data set consists of 250 cases. Analysis was limited to cases with transitive price preferences.
#> (Removed: n = 125 / 50% of data)