PAPER "On the similarity between exchangeable profiles .."

PAPER "On the similarity between exchangeable profiles: A psychometric model, analytic strategy, and empirical illustration"

ABSTRACT: Analyses of profile similarity are widespread in personality psychology, but their apparent simplicity masks difficult psychometric and statistical issues. We present a psychometric framework that addresses an important challenge (i.e., profile normativeness) in examinations of dyadic exchangeable profiles. In addition, we present an analytic strategy accounting for non-independence that often arises in analyses of profile similarity, facilitating integrated examinations of variables at dyadic and individual levels. An empirical analysis of personality similarity and relationship quality demonstrates that the model and analytic strategy can reveal novel psychological insights. These are important advances, as previous work has ignored exchangeable profiles and has failed to present an integrated psychometric and statistical framework for profile similarity.

Furr (2008) presented a psychometric model focusing on three concepts relevant in almost any examination of profile similarity.
Overall Similarity is the degree to which two profiles are similar to each other (with no adjustment for normativeness), computed as the correlation or covariance between two profiles.
Normativeness is the degree to which an individual profile is like an average profile (e.g., the degree to which a given wife is like the normative or average wife), and it is computed as the correlation or covariance between an individual's profile and a relevant "normative" profile of means. Normativeness is indexed independently for both partners in the dyad (i.e., how normative is partner 1's profile? How normative is partner 2's profile?).
Distinctive Similarity is a normatively-adjusted index reflecting the degree to which two profiles are uniquely similar to each other, in terms of the ways in which they are "distinct" from the average persons.

For online dating applications and personality based recommenders the above paper is not useful because daters are "distinguishable" instead of "exchangeable".

Similarity is a word that has different meanings for different persons or companies, it exactly depends on how mathematically is defined. I calculate overall similarity in personality patterns with (a proprietary) pattern recognition by correlation method. It takes into account the score and the trend to score of any pattern.

In compatibility matching methods there are 2 steps:
1) to objectively measure personality traits (with the 16PF5 test or similar) without distortion.
2) to calculate compatibility (personality similarity) between prospective mates

To calculate personality similarity between daters, the key is the ENSEMBLE!

BRA (#X/ means person #X's 16PF5 Report
KET /#Y) means person #Y's 16PF5 Report
/CQ/ means Comparison Operator

For person #X:: A:6.B:7.C:6.E:8.F:9.G:6.H:7.I:7.L:8.M:7.N:2.O:5.Q1:8.Q2:7.Q3:3.Q4:4
16 distinguishable particles in a one_dimensional box of length L and infinite outside the box with 10 quantized levels of energy (named box X)
distinguishable particle (A) Warmth at level "6"
distinguishable particle (B) Reasoning at level "7"
distinguishable particle (C) Emotional Stability at level "6"
distinguishable particle (E) Dominance at level "8"
distinguishable particle (F) Liveliness at level "9"
distinguishable particle (G) RuleConsciousness at level "6"
distinguishable particle (H) Social Boldness at level "7"
distinguishable particle (I) Sensitivity at level "7"
distinguishable particle (L) Vigilance at level "8"
distinguishable particle (M) Abstractedness at level "7"
distinguishable particle (N) Privateness at level "2"
distinguishable particle (O) Apprehension to Change at level "5"
distinguishable particle (Q1) Openness at level "8"
distinguishable particle (Q2) SelfReliance at level "7"
distinguishable particle (Q3) Perfectionism at level "3"
distinguishable particle (Q4) Tension at level "4"

And

For person #Y:: A:5.B:7.C:4.E:8.F:7.G:4.H:5.I:6.L:4.M:6.N:8.O:9.Q1:6.Q2:8.Q3:4.Q4:4
16 distinguishable particles in other one_dimensional box of length L and infinite outside the box with 10 quantized levels of energy (named box Y)
distinguishable particle (A) Warmth at level "5"
distinguishable particle (B) Reasoning at level "7"
distinguishable particle (C) Emotional Stability at level "4"
distinguishable particle (E) Dominance at level "8"
distinguishable particle (F) Liveliness at level "7"
distinguishable particle (G) RuleConsciousness at level "4"
distinguishable particle (H) Social Boldness at level "5"
distinguishable particle (I) Sensitivity at level "6"
distinguishable particle (L) Vigilance at level "4"
distinguishable particle (M) Abstractedness at level "6"
distinguishable particle (N) Privateness at level "8"
distinguishable particle (O) Apprehension to Change at level "9"
distinguishable particle (Q1) Openness at level "6"
distinguishable particle (Q2) SelfReliance at level "8"
distinguishable particle (Q3) Perfectionism at level "4"
distinguishable particle (Q4) Tension at level "4"

Each quantized level is associated with a probability density function.
(#X/CQ/#Y) is the sum of the comparisons between different states, the sum of partial probabilities.
(#X/CQ/#Y) == 74.79865772%
Read as the pattern 6.7.6.8.9.6.7.7.8.7.2.5.8.7.3.4 is 74.79865772% similar to the pattern 5.7.4.8.7.4.5.6.4.6.8.9.6.8.4.4

Online Dating sites and Personality Based recommenders have very big databases, in the range of 20 000 000 (twenty million) profiles, so the Big 5 model is not enough for predictive purposes.
If they use the Big 5 model, the whole precision is less than you could achieve searching by your own!!!
NORMATIVE personality tests like Big5 versions used at PlentyOfFish, eHarmony , Meetic Affinity, Parship, Be2, True are good for guidance (orientation) purposes but not good enough for predictive purposes.
"Because the Big Five groups the more specific primary-level factors, feedback organized around the five Global Factor scales is more easily understood. For detailed feedback or predictive purposes, one should assess the more specific primary factors. Research has shown that more specific factors like the primary scales of the 16PF Questionnaire predict actual behavior better than the Big 5 Global Factors. For example, one extravert (a bold, fearless, high-energy type) may differ considerably from another (a sweet, warm, sensitive type), depending on the extraversion-related primary scale score patterns, so deeper analysis is typically warranted." Extracted from the 16PF5 Manual


 WorldWide, there are over 5,000 -five thousand- online dating sites
but no one is using the 16PF5 (or similar) to assess personality of its members!
but no one calculates similarity with a quantized pattern comparison method!
but no one can show Compatibility Distribution Curves to each and every of its members!
but no one is scientifically proven! The only way to revolutionize the Online Dating Industry is using the 16PF5 normative personality test, available in different languages to assess personality of members, or a proprietary test with exactly the same traits of the 16PF5 and expressing compatibility with eight decimals (needs a quantized pattern comparison method, part of pattern recognition by cross-correlation, to calculate similarity between prospective mates.)
High precision in matching algorithms is precisely the key to open the door and leave the infancy of compatibility testing.
It is all about achieving the eighth decimal!
With 8 decimals, you have more precision than any person could achieve by searching on one's own, but the only way to achieve the eighth decimal is using analysis and correlation with quantized patterns.
Without offering the NORMATIVE16PF5 (or similar test measuring exactly the 16 personality factors) for serious dating, it will be impossible to innovate and revolutionize the Online Dating Industry All other proposals are NOISE and perform as placebo.


Please read also
How to calculate personality similarity between users .
An exercise of similarity.
How LIFEPROJECT METHOD calculates similarity. 
STRICT PERSONALITY SIMILARITY by LIFEPROJECT METHOD.
Personality Distribution Curves using the NORMATIVE 16PF5.
ALGORITHMS & POWER CALCULATION.
Innovations: to take the 16PF5 test 3 times.
Why your brain distorts!