Person-Target Profiling Issues in Matching and ...A profile is defined by Collins English Dictionary...

Paul Barrett

Psytech International (UK) University of Auckland University of CanterburyFaculty of Business Department of Psychology

[email protected] [email protected] [email protected]

Web: www.pbarrett.net

Paul Barrett

Psytech International (UK) University of Auckland University of CanterburyFaculty of Business Department of Psychology

[email protected] [email protected] [email protected]

Web: www.pbarrett.net

Consumer Personality & Research 2005 Conference, September 20-24th, 2005, Dubrovnik

Basic Definitions

A profile is defined by Collins English Dictionary (1991,3rd edition) as: "a graph, "a graph, table, or list of scores representing the extent to table, or list of scores representing the extent to which a person, field, or object exhibits various which a person, field, or object exhibits various tested characteristics or tendencies"tested characteristics or tendencies".

Cronbach and Gleser (1953) introduced three terms to describe a profile:

ElevationElevation: the mean of all scores within a single profile.

Scatter /Variability Scatter /Variability : the square root of the sum of squares of a single profile's deviation scores about the Elevation for that profile. Essentially the standard deviation of scores within a profile, multiplied by the square root of the number of attributes constituting the profile.

Shape Shape : the residual information left in each score of a profile, after equating for the elevation and scatter indexes by subtracting out the elevation and dividing the resultant deviation score by the scatter value.

Basic Definitions

The Vector ProfileTwo Profiles - Raw scale scores

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Scale Scores Target Scale Scores

Elevation Subtracted profiles

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Elevation Subtracted Target Elevation Subtracted

The Vector Profile

Scatter Normalised profiles

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Scatter Normalised Target Scatter Normed

The Vector Profile

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Frequency in a Working Day-2

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2Preference for Work-Style

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3D Profile: showing bipolar nonlinear categorical scoring

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3D Attribute Weight x Job Performance x Preference for Work-Type

Two Profiles - Raw scale scores

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Hypothesised, “idealideal” profileSingle empirical profile – the “star performerstar performer”Homogenous empirical profile – the

construction of a single “homogenous group homogenous group profileprofile” from a group of individuals who are all adjudged to be homogenous with respect to some external criterion (such as their job, level within a company, gender, team position, brand purchase etc.)

Constructing the Target Vector Profile


Although the vast majority of simple vector homogenous group profiling applications use a single point-estimate as the target magnitude, a ““homogenous with respect to a criterionhomogenous with respect to a criterion”” group target profile attribute should also take into account the “variability” of each estimate…

PointPoint--estimate and attribute variabilityestimate and attribute variability


The mean and median point-estimates and their disparity.

The interquartile and full magnitude range.A 10% modal range around the medianThe reliability/reproducibility of an

attribute score

And a suitable algorithm to incorporate the profile attribute reliability/variability into the matching procedures!

Profile Matching

TLabelY

BLabelY

PF Low Score Desc High Score Desc

A Reserved Outgoing

C Temperamental Calm-Stable

E Accomodating Assertive

F Cautious Enthusiastic

G Expedient Conscientious

H Retiring Socially Bold

I Factual Intuitive

L Trusting Suspicious

M Practical Conceptual

N Direct Restrained

O Confident Self Doubting

Q1 Conventional Radical

Q2 Group-orientated Self-Sufficient

Q3 Informal Disciplined

Q4 Relaxed Tense-Driven

1 2 3 4 5 6 7 8 9 10

15FQ Job Match

ComparisonFunction

Ranked Respondentsin terms of nearness to Target Profile

Target Profile

Profile Matching

1st rule of profile matching11stst rule of profile matchingrule of profile matching

Never use a matching coefficient without at first examining exhaustively how it will function on random, typical, and specifically degraded profile data.

Profile Matching

Transformation SensitivityTransformation Sensitivity

Determine the sensitivity of a coefficient to differences between the target and comparison profile elevationelevation(level) and scatterscatter (variability) whilst preserving an almost identical profile shape.

Profile Matching

The Sampling DistributionThe Sampling Distribution

Determine the expected average size and frequency distribution for a coefficient, using two kinds of applicationapplication--specificspecific* magnitude scaled data:

Random Profile VectorsTypical Profile Vectors

* Using the actual magnitude ranges for variables which are to beconsidered typical for your application.

Profile Matching

Systematic Profile Systematic Profile DegredationDegredation

Determine the sensitivity of a coefficient to systematically graduated systematically graduated disparitydisparity between a target and comparison profile.

Profile Matching

0.990.990.99De-Scatter comparison

0.780.790.99De-Elevation comparison

0.780.350.99Raw profile comparison

ICC Model 3

ICC Model 2

Pearson r


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Profile Matching

0.990.9997.0%De-Scatter comparison

0.640.9985.7%De-Elevation comparison

-0.201.070.9%Raw profile comparison

CattellProfile

SimilarityCongruence

NormalizedEuclidean Similarity


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Profile Matching

The coefficient distribution analyzer

The Sampling DistributionsThe Sampling Distributions

Profile Matching

Always work with the data that represent the profiles being compared. Transforming to rank values or standardized scores removes important discrepancy information.

2nd rule of profile matching22ndnd rule of profile matchingrule of profile matching

Profile Matching

www.pbarrett.net/statistics_corner.htmDocument = Euclidean Distance: Raw, Normalised, and Double-Scaled Coefficients.

Double Scaled Distance (DSD)

Profile Matching

A distance (or similarity) coefficient which is easily interpretable.

A fixed 0-1 metric achieved using linear transformations of discrepancy data.

Is comparable in meaning across all possible varying variable-range magnitudes.

Double Scaled Distance (DSD)

Profile Matching

DoubleDouble--Scaled Euclidean DistanceScaled Euclidean Distance

Step 1: Determine the maximum possible squared discrepancy for each variable comparison using the minimum and maximum possible values for this variable. Call these values md. Each variable will possess a minimum and maximum so the md for each variable is just:

mdi = (Max for variable i – Min for variable i)2

Profile MatchingStep 2. Compute a squared discrepancy, divide it by the maximum possible discrepancy for that particular comparison, then take the square root of the sum to produce the single-scaled variable Euclidean distance.

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i i

p pdmd=

⎛ ⎞−= ⎜ ⎟

⎝ ⎠∑

where p1i = the attribute i value for person 1p2i = the attribute i value for person 2

d1 = the “scaled variable” Euclidean distancemdi = the maximum possible squared discrepancy

per variable i of v variables.

Profile Matching

Compute the scaled value from step 2 by dividing d1 by , where v = the number of variables.

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Profile Matching

When you can’t find a existing coefficient that appears to work the way you want it to – design a new one that does exactly what you want it to – and innovateinnovate.

3rd rule of profile matching33rdrd rule of profile matchingrule of profile matching

Profile Matching

www.pbarrett.net/factor_similarity.htmwww.pbarrett.net/factor_similarity.htm

Kernel Smoothed Distance (KSD)

More details can be found in the manual to the Orthosim_2Orthosim_2 Congruential Coordinate Similarity Program.

Profile Matching

A similarity coefficient which is easily interpretable, has a fixed 0-100% metric, and is comparable in meaning across all possible varying variable-range magnitudes.

I want to be able to calibratecalibrate this coefficient to give me values which best represent what I see visually when looking at profiles, and where I can adjust its characteristics to be more or less sensitive to observed profile discrepancies (in a false-positive/negative cost-benefit scenario analysis)

Profile Matching

The Standard Normal probability density function (the kernel kernel function) is:

( )222

where the population standard deviation = 1.0

the population mean = 0.0

the value of pi (3.141593)

euler's e (2.718282

12

= =

= e = )

x

ordz eμσ

σ πσμπ

⎡ ⎤−⎢ ⎥−⎢ ⎥⎣ ⎦=

Profile Matching: KSD with SD = 10

Profile Matching: KSD with SD = 30

Profile Matching

So, assume we have a target profiler value of 50, with an observed value (x) of 50, the ordinate expression for this difference is computed as:

( )22

50 502 10

where the population standard deviation = 10.0

the population mean (our target value) = 50.0

the value of pi (3.141593)

1 0.039894210 2

= =

=

ordz eπ

σμπ

⎡ ⎤−⎢ ⎥−⎢ ⎥⋅⎣ ⎦= =

an observed preference value (= 50 here also) = x

Profile Matching

( )

( )( )2

22

standard devation unit

person profile attribute value

target profile attribut

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KSD e

pt

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σ

⎡ ⎤−⎢ ⎥−⎢ ⎥⎣ ⎦

⎡ ⎤⎢ ⎥= ⋅ ⋅ ⋅⎢ ⎥⎢ ⎥⎣ ⎦

===

Profile Matching

97.0%99.99%99.99%De-Scatter comparison

85.7%55.6%86.5%De-Elevation comparison

70.9%4.9%42.9%Raw profile comparison

1-DSDKSD with

SD=2KSD with

SD = 5


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Profile Matching

Essentially, the KSD coefficient is a “designerdesigner--mediatedmediated” coefficient. That is, its value range is constructed or calibrated calibrated to suit the particular decision-requirements and error-costs defined for a specific application.

2-sten difference

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Cattell rp = 0.28Pearson r = 1.001-Alienation = 0.85Intraclass-2 = 0.721-DSD = 77.8%KSD (sd=1.67) = 48.7%


All scales exactly the same - except the first (2 vs 10)

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Cattell rp = – 0.20Pearson r = 0.291-Alienation = 0.47Intraclass-2 = 0.271-DSD = 63.7%KSD (sd=1.67) = 83.7%


All scores exactly the same - except the first (2 vs 10)

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All scores exactly the same - except for first (2 vs 10)

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Classifier Predictive-Function Modelling

ClassifierFunction

The goal is to construct a classifier or some function of a set of variables which predict a predefinedpredefined criterion group membership

Inductive Homogeneity Analysis

Inductive ClassifierFunction

The goal is to discoverdiscoverhomogenous groups or clusters within a set of individuals or objects

What if we let the respondent define their own profile as a “conceptual wholeconceptual whole”or “attribute mapattribute map”, rather than the investigator reconstruct this post-assessment?

Graphical ProfilingGraphical ProfilingGraphical Profiling

Construct an assessment which consists of displaying a single, precisely semantically defined “construct” to a respondent, who then performs a rating of an object or person against it.

Allow a respondent to rate attributes on a magnitude scale, with immediate “visual relativityvisual relativity” maintained with all other previously or to-be-rated attributes.

Rate in 1 or 2 dimensions simultaneously.Marked response graduation is optional.Relevant only to non-cognitive preference,

self-report, or 360-style peer-review ratings.Only realistically possible via

computer/PDA-based administration.

Graphical ProfilingGraphical ProfilingGraphical Profiling

Graphical Profiling – 1-D Personality

Using the free 5-factor personality model item-bank at the International Personality Item Pool

http://ipip.ori.org/ipip/

Specifically using 1010 facets taken from the AB5C 45-facet personality questionnaire as “typical” personality test scales, spanning about 106 questionnaire items106 questionnaire items in total …http://ipip.ori.org/ipip/newAB5CTable.htm

Happiness

Impulse-Control

CalmnessFactor 4: Emotional StabilityOrderliness

Organization

Purposefulness

EfficiencyFactor 3: ConscientiousnessTalkativeness

Leadership

FriendlinessFactor 1: ExtraversionFacetFactor


Extract the meaning of all the items in a scale, and compose a single rating statement that seems to best encompass the meaning not only of the scale name, but that embodied within the items.


Construct the meaning of Construct the meaning of the construct to be ratedthe construct to be rated

Dislike talking about myself.X212Speak softly.H548Demand to be the centre of interest.H769Make a lot of noise.H531Never stop talking.H536Like to attract attention.H1150Make myself the centre of attention.H535Speak loudly.H527Talk too much.H1138Do most of the talking.H4

single item rewords? ... facet = TalkativeTalkative


The Rating Statement: TalkativeTalkative“I have no problem in talking about almost anything. In fact, I find it hard to stop sometimes, especially if I've become the centre of attention! Frankly, I just like talking with people”.


The Personality Profiler


36.734.1Leadership

39.335.7Happiness

33.737.2Impulse-Control

33.536.4Calmness

32.532.9Orderliness

42.546.7Organization

44.441.5Purposefulness

41.537.7Efficiency

33.327.1Talkativeness

39.335.3Friendliness

Profiler Scores

AB5C Scales

Profiler -vs-

questionnairescale-score

MeansMeans

N=99 cases

8.86.9Leadership

6.76.9Happiness

11.36.9Impulse-Control

9.36.1Calmness

10.58.3Orderliness

10.87.3Organization


9.67.7Efficiency

9.97.3Talkativeness

8.16.8Friendliness

Profiler Scores

AB5C Scales

Profiler -vs-

questionnairescale-score

Std. Std. DevnsDevns..

N=99 cases

0.590.54Leadership

0.690.64Happiness

0.320.280.28Impulse-Control

0.620.54Calmness

0.800.75Orderliness

0.650.60Organization


0.680.63Efficiency

0.750.70Talkativeness

0.770.71Friendliness

Disattenuated

Actual Correlation

Profiler -vs-

questionnairescale-scores

CorrelationsCorrelations

N=99 cases

Predicting AB5C Scale "Leadership" by Profiler Score Plotting Prediction Residuals by Profiler Score

10 15 20 25 30 35 40 45 50 55

Personality Profiler Score

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Res

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lsGraphical Profiling – 1-D Personality

Completion Times and Preference

Questionnaire: about 2020 minutesProfiler: about 55 minutes

•• 93%93% of individuals preferred completing the Profiler assessment over the paper and pencil Questionnaire.•• 87%87% felt they were able to describe themselves adequately using it.


Graphical Profiling – 2-D Work Preferences

The movie


( ) ( ) ( )( ) ( ) ( )

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1

100 0.25 0.25 0.5

10 30 60 600 50 0.25 80 0.25 80 0.5 80%

jki i j i k i j i k ij ik

jk

Match a a a a f f

Match

⎡ ⎤= − − ⋅ + − ⋅ + − ⋅⎣ ⎦⎡ ⎤= − − ⋅ + − ⋅ + − ⋅ =⎣ ⎦

The original Mariner7 person-to-person match coefficientP

refe

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r

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Clarity p1

Clarity p2

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euclideandistance

euclideandistance

Using 2131 real-data cases, I compared every individual’s profile with every other individual (2.2million match coefficients) – and looked at the expected-value frequency distributions …

Mariner 7 scaled, weighted, unsigned simple discrepancy coefficient

Weighted normalised euclidean expressed as % similarity

Pref

eren

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or

Frequency20

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100

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Ambiguity p2

Clarity p1

Clarity p2

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euclideandistance

euclideandistance

k1

k2

k1-freq

k2-freq

Weighted, normalised, doubly-degraded euclidean expressed as % similarity

Coefficient Density as a function of Profile Elements


Let the specific application requirements determine the optimal profile matching index.Algorithmic profiling solutions are always going to be optimal – but will require calibration and exhaustive scenario testing.Graphical Profiler assessment is “intriguing” but remains a relatively underdeveloped assessment methodology.

Person-Target Profiling Issues in Matching and ...A profile is defined by Collins English Dictionary...

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Transcript of Person-Target Profiling Issues in Matching and ...A profile is defined by Collins English Dictionary...