CN111833990A - Method for filling missing items of psychological assessment scale - Google Patents

Method for filling missing items of psychological assessment scale Download PDF

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CN111833990A
CN111833990A CN202010692640.9A CN202010692640A CN111833990A CN 111833990 A CN111833990 A CN 111833990A CN 202010692640 A CN202010692640 A CN 202010692640A CN 111833990 A CN111833990 A CN 111833990A
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王雄
任朝俊
任婧
徐世中
王晟
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University of Electronic Science and Technology of China
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    • G16H—HEALTHCARE INFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR THE HANDLING OR PROCESSING OF MEDICAL OR HEALTHCARE DATA
    • G16H20/00—ICT specially adapted for therapies or health-improving plans, e.g. for handling prescriptions, for steering therapy or for monitoring patient compliance
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Abstract

The invention discloses a method for filling missing items of a psychological assessment scale, which comprises the steps of establishing a two-dimensional matrix R according to the existing psychological assessment scale of a plurality of similar assessment objects, wherein the two-dimensional matrix R comprises the assessment objects and assessment items; then, according to the existing data of the two-dimensional matrix R, the similarity S between the evaluation object u and other evaluation objects v is calculateduvClassifying the objects with close similarity into the same group of evaluation objects; and then calculating the score of the missing item j of the evaluation object u in the same group of evaluation objects according to an interpolation method. According to the method, the missing items are filled by utilizing the similarity between similar evaluation objects according to the existing evaluation scale with missing data, and the data is completely filled.

Description

Method for filling missing items of psychological assessment scale
Technical Field
The invention relates to the technical field of psychological assessment, in particular to a missing item filling method for a psychological assessment scale.
Background
The psychological assessment scale is called psychological measurement, and means that a numerical quantification value is determined according to a certain psychological theory and by using a certain operation program according to psychological characteristics and behaviors of people such as ability, personality, psychological health and the like. The psychological state of the person can be evaluated according to the quantified value evaluated by the scale. A complete psychology evaluation scale is usually composed of a plurality of evaluation dimensions, each evaluation dimension evaluates against one dimension of psychology, and each dimension evaluation also comprises a plurality of items. For example, in order to evaluate the problem of rethinking of full criminal releasers, prisons in China mostly use a 'Chinese criminal psychological test personality examination' (COPA-PI) scale to perform psychological evaluation on full criminal releasers so as to evaluate the risk of rethinking of the full criminal releasers. The COPA-PI scale contains 13 dimensions: (1) the inner and outer inclination contain 10 items; (2) emotional stability, 10 items total; (3) consanguinity, 8 items in total; (4) impulsivity, 10 items in total; (5) a total of 8 items; (6) reporting performance, 10 items in total; (9) self-confidence, 10 items in total; (10) anxiety, 10 items in total; (11) intelligence, 10 items in total; (12) psychotropic tendencies, 14 items in total; (13) crime thinking model, 10 items in total. Each item of the psychological evaluation scale corresponds to a selection topic, and different selections made by an evaluator correspond to specific quantitative values evaluated by the item.
In the actual psychological evaluation process, the partial values in the evaluation scale may be missing or invalid due to some objective reasons (e.g., missing information) or mismatch of evaluation objects, so that the evaluation result is inaccurate or cannot be evaluated.
Disclosure of Invention
The invention aims to provide a method for filling missing items in a psychological assessment scale, which fills the missing items by utilizing the similarity between similar assessment objects according to the existing assessment scale with missing data, and completely fills the data.
The invention is realized by the following technical scheme:
a method for filling missing items in a psychological assessment scale comprises the following steps:
s1, establishing a two-dimensional matrix R according to the existing psychological assessment scale of a plurality of similar assessment objects, wherein the two-dimensional matrix R comprises the assessment objects and assessment items;
s2, calculating the similarity S between the object u to be evaluated and other objects v to be evaluated according to the existing data of the two-dimensional matrix Ruv，SuvThe formula of (c) is shown as follows:
Figure BDA0002589799150000011
in the formula, I (u, v) represents a project set which is evaluated by both the object u and v to be evaluated, and alpha is a constant parameter;
s3, mixing SuvSorting the similarity according to the sorting sequence from high to low, and selecting the first K evaluation objects to be added into the set N (u);
wherein, N (u) represents an evaluation object set with higher similarity to the evaluation object to be tested; k represents the number of evaluation targets in the set;
s4, calculating the score of the missing item j of the evaluation object u according to an interpolation method, wherein the calculation process is shown as the following formula:
Figure BDA0002589799150000021
in the formula (I), the compound is shown in the specification,
Figure BDA0002589799150000022
is a missing term rujInterpolation of (w)uvRepresenting the interpolation weight of the object v to be evaluated to the object u to be evaluated;
s5, obtaining interpolation weight w according to matrix and vector solutionuvInterpolation weight wuvAnd (3) calculating the score of the evaluation object u missing item j in the formula (2).
Using a certain scale to psychologically evaluate several persons, the scores of the evaluated persons on each project can be represented by using a two-dimensional matrix R, wherein the element of the u-th row and the j-th column of the matrix is RujAnd the score value of the evaluation object u on the jth evaluation item is shown. When some evaluation object has missing items, filling the missing items by utilizing the similarity between similar evaluation objectsAnd (6) charging.
The conception of the invention is as follows: and establishing a two-dimensional matrix R according to the existing psychological assessment tables of a plurality of similar assessment objects, and calculating part of unknown values according to the existing values in the two-dimensional matrix R.
The similarity of the evaluation objects is calculated through the constructed two-dimensional matrix R and is grouped, the evaluation objects with high similarity are defined as a group of similar evaluation objects, missing values in partial evaluation items are calculated in the group of similar evaluation objects according to existing values in the two-dimensional matrix R, namely the missing items are filled by utilizing the similarity among similar evaluation objects, and the data is completely filled.
Further, the optimal interpolation weight is obtained according to the least square method as shown in the following formula:
minw∑i≠j(rui-∑v∈N(u)wuvrvi)2(3)
according to the statistical principle, the equation (3) is equivalent to a linear regression equation, which is shown as the following equation:
Aw＝b (4)，
where A is a K matrix and the b vector is obtained by a two-dimensional matrix R.
Further, when the data in the two-dimensional matrix R is a dense scene, the element a in the matrix avmIs defined as:
Avm＝∑i≠jrvirmi(5)
wherein v, m ∈ N (u);
similarly, the vector b ∈ RKIs defined as:
bv＝∑i≠jrvirui(6)
wherein v ∈ N (u).
Further, when the data in the two-dimensional matrix R is a sparse scene, the method uses
Figure BDA0002589799150000031
Matrix sum
Figure BDA0002589799150000032
To approximate the a matrix and the b vector respectively,
Figure BDA0002589799150000033
matrix sum
Figure BDA0002589799150000034
The vector is defined as follows:
Figure BDA0002589799150000035
wherein v, m ∈ N (u);
Figure BDA0002589799150000036
wherein v ∈ N (u);
for each pair of evaluation objects (v is equal to N (u), and m is equal to N (u), the formula (7) is used for calculating
Figure BDA0002589799150000037
Straight then according to
Figure BDA0002589799150000038
Avg is calculated as follows:
Figure BDA00025897991500000318
approximate A matrix and b vector as
Figure BDA0002589799150000039
Matrix sum
Figure BDA00025897991500000310
Vector, then there are:
Figure BDA00025897991500000311
wherein v, m ∈ N (u), avg is allβ is a constant controlling the scaling;
Figure BDA00025897991500000313
wherein v, m ∈ N (u); avg is all
Figure BDA00025897991500000314
β is a constant controlling the scaling;
Figure BDA00025897991500000315
matrix sum
Figure BDA00025897991500000316
The vectors are approximations of the A matrix and the b vector respectively, and the expression of the optimal interpolation weight is optimized as shown in the following formula:
Figure BDA00025897991500000317
the intensive scene specifically means that the neighbor of the evaluation object u effectively evaluates the projects except the project j; the sparse scene specifically means that K neighbors of the test object u lack data of a plurality of evaluation items.
Compared with the prior art, the invention has the following advantages and beneficial effects:
the similarity of the evaluation objects is calculated through the constructed two-dimensional matrix R and is grouped, the evaluation objects with high similarity are defined as a group of similar evaluation objects, missing values in partial evaluation items are calculated in the group of similar evaluation objects according to existing values in the two-dimensional matrix R, namely the missing items are filled by utilizing the similarity among similar evaluation objects, and the data is completely filled.
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The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a flowchart of the sparse scene missing item calculation according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not meant to limit the present invention.
Example 1:
as shown in fig. 1, a method for filling missing items in a psychological assessment scale comprises the following steps:
s1, establishing a two-dimensional matrix R according to the existing psychological assessment scale of a plurality of similar assessment objects, wherein the two-dimensional matrix R comprises the assessment objects and assessment items, and is shown in Table 1:
TABLE 1
Figure BDA0002589799150000041
In table 1, the symbol "x" represents a missing item present in the evaluation object. Considering that in the actual evaluation process, one evaluation object in a group of evaluation objects often has a plurality of evaluation objects with similar psychological states to the evaluation object, and persons with similar psychological states may give very similar selections to the same evaluation item, that is, the evaluation objects have similar scores on the same evaluation item. Based on the principle, the j-th unknown score r of the evaluation object u is filledujThen, the scores of other persons to be evaluated similar to u on the j-th project can be used for deducing ruj；
S2, calculating the similarity S between the object u to be evaluated and other objects v to be evaluated according to the existing data of the two-dimensional matrix Ruv，SuvThe formula of (c) is shown as follows:
Figure BDA0002589799150000042
the formula (1) is a self-defined calculation model capable of reflecting the similarity between the objects, and the missing value of the object to be evaluated is complemented by using the approximate object.
In the formula, I (u, v) represents a project set which is evaluated by both the object u and v to be evaluated, and alpha is a constant parameter;
s3, mixing SuvSequencing the similarity according to the sequence from high to low, and selecting the first K evaluation objects to be added into the set N (u), wherein K is a constant parameter;
wherein, N (u) represents an evaluation object set with higher similarity to the evaluation object to be tested; k represents the number of evaluation targets in the set;
in order to vividly describe the above similarity formula, taking table 2 as an example, a detailed explanation is made: assuming that α is 1 and K is 2, the following table has six evaluation objects, each of which has a missing value, and the object number 1 is used as the research object, in this example, the number of commonly evaluated items | I (u, v) | is 3 (for example, similarity between object numbers 1 and 2 is calculated, scores 3 and 4 are not commonly evaluated because of missing, commonly measured items are "score 125", similarity between 1 and 4 is calculated similarly, and commonly evaluated items are "score 235"), and similarity is S according to the similarity formula12＝3/((10-9)2)+(2-3)2+(8-7)2+1) ═ 3/4, likewise, S13＝3/42、S14＝3/42、S15＝1/3、S16Since the similarity of the evaluation target increases as the numerical value increases 3/44, N (1) should be {2, 5 }. The obtained object number {1, 2, 5} can be defined as a group of similar evaluation objects, {3, 4, 6} can be defined as a group of similar evaluation objects;
TABLE 2
Figure BDA0002589799150000051
S4, according to the similarity between any two evaluation objects u and v, the similarity S between each evaluation object u and any other evaluation object v can be easily calculateduvAnd K evaluation object sets N (u) most similar to u) And then, calculating the score of the missing item j of the evaluation object u according to an interpolation method, wherein the calculation process is shown as the following formula:
Figure BDA0002589799150000052
in the formula (I), the compound is shown in the specification,
Figure BDA0002589799150000053
is a missing term rujInterpolation (estimation), wuvRepresenting the interpolation weight of the object under evaluation v to the object under evaluation u, obviously, the interpolation error
Figure BDA0002589799150000054
The smaller the better, the interpolation weight w in equation (2) is optimized to reduce the interpolation erroruv；
S5, obtaining interpolation weight w according to matrix and vector solutionuvInterpolation weight wuvCalculating the score of the evaluation object u missing item j in the formula (2); the optimal interpolation weight is obtained according to the least squares method as shown in the following formula:
minw∑i≠j(rui-∑v∈N(u)wuvrvi)2(3)
according to the statistical principle, the equation (3) is equivalent to a linear regression equation, which is shown as the following equation:
Aw＝b (4)，
where A is a K matrix and the b vector is obtained by a two-dimensional matrix R.
When the data in the two-dimensional matrix R is a dense scene, the element A in the matrix AvmIs defined as:
Avm＝∑i≠jrvirmi(5)
wherein v, m ∈ N (u);
similarly, the vector b ∈ RKIs defined as:
bv＝∑i≠jrvirui(6)
wherein v ∈ N (u);
the optimal interpolation weight vector w can be found by solving equation (4): finally, the evaluation value of the defect can be estimated by using the formula (2)
Figure BDA0002589799150000061
The optimal interpolation weight vector calculation is shown in table 3:
TABLE 3
Figure BDA0002589799150000062
Figure BDA0002589799150000071
Example 2:
the present embodiment is based on embodiment 1, and is different from the embodiment in that when the data in the two-dimensional matrix R is a sparse scene, the sparse scene is used
Figure BDA0002589799150000072
Matrix sum
Figure BDA0002589799150000073
To approximate the a matrix and the b vector respectively,
Figure BDA0002589799150000074
matrix sum
Figure BDA0002589799150000075
The vector is defined as follows:
Figure BDA0002589799150000076
wherein v, m ∈ N (u);
Figure BDA0002589799150000077
wherein v ∈ N (u);
evaluating each pair of objects (v is equal to N (u), m is equal to N (u)N (u) is calculated using the formula (7)
Figure BDA0002589799150000078
Straight then according to
Figure BDA0002589799150000079
The value avg is calculated as follows:
Figure BDA00025897991500000710
approximate A matrix and b vector as
Figure BDA00025897991500000711
Matrix sum
Figure BDA00025897991500000712
Vector, then there are:
Figure BDA00025897991500000713
wherein v, m ∈ N (u), avg is all
Figure BDA00025897991500000714
β is a constant controlling the scaling;
Figure BDA0002589799150000081
wherein v, m ∈ N (u); avg is all
Figure BDA0002589799150000082
β is a constant controlling the scaling;
Figure BDA0002589799150000083
matrix sum
Figure BDA0002589799150000084
The vectors are approximations of the A matrix and the b vector, respectively, and are optimally interpolatedThe expression optimization of the value weights is shown as follows:
Figure BDA0002589799150000085
the optimal interpolation weight vector w can be obtained by solving the formula (12); finally, the evaluation value of the defect can be estimated by using the formula (2)
Figure BDA0002589799150000086
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (4)

1. A method for filling missing items in a psychological assessment scale is characterized by comprising the following steps:
s1, establishing a two-dimensional matrix R according to the existing psychological assessment scale of a plurality of similar assessment objects, wherein the two-dimensional matrix R comprises the assessment objects and assessment items;
s2, calculating the similarity S between the object u to be evaluated and other objects v to be evaluated according to the existing data of the two-dimensional matrix Ruv，SuvThe formula of (c) is shown as follows:
Figure FDA0002589799130000011
in the formula, I (u, v) represents a project set which is evaluated by both the object u and v to be evaluated, and alpha is a constant parameter;
s3, mixing SuvSorting the similarity according to the sorting sequence from high to low, and selecting the first K evaluation objects to be added into the set N (u);
wherein, N (u) represents an evaluation object set with higher similarity to the evaluation object to be tested; k represents the number of evaluation targets in the set;
s4, calculating the score of the missing item j of the evaluation object u according to an interpolation method, wherein the calculation process is shown as the following formula:
Figure FDA0002589799130000012
in the formula (I), the compound is shown in the specification,
Figure FDA0002589799130000013
is a missing term rujInterpolation of (w)uvRepresenting the interpolation weight of the object v to be evaluated to the object u to be evaluated;
s5, obtaining interpolation weight w according to matrix and vector solutionuvInterpolation weight wuvAnd (3) calculating the score of the evaluation object u missing item j in the formula (2).
2. The method for filling missing items in a psychological assessment scale according to claim 1, wherein the optimal interpolation weight is obtained according to the least square method as shown in the following formula:
minw∑i≠j(rui-∑v∈N(u)wuvrvi)2(3)
according to the statistical principle, the equation (3) is equivalent to a linear regression equation, which is shown as the following equation:
Aw＝b (4)，
where A is a K matrix and the b vector is obtained by a two-dimensional matrix R.
3. The method for filling missing items in mental measurement scale according to claim 2, wherein when the data in the two-dimensional matrix R is dense scene, the element A in the matrix A isvmIs defined as:
Avm＝∑i≠jrvirmi(5)
wherein v, m ∈ N (u);
similarly, the vector b ∈ RKIs defined as:
bv＝∑i≠jrvirui(6)
wherein v ∈ N (u).
4. The method for filling missing items in psychological assessment scale according to claim 2, wherein when the data in the two-dimensional matrix R is sparse scene, the method uses
Figure FDA0002589799130000021
Matrix sum
Figure FDA0002589799130000022
To approximate the a matrix and the b vector respectively,matrix sum
Figure FDA0002589799130000024
The vector is defined as follows:
Figure FDA0002589799130000025
wherein v, m ∈ N (u);
Figure FDA0002589799130000026
wherein v ∈ N (u);
for each pair of evaluation objects (v is equal to N (u), and m is equal to N (u), the formula (7) is used for calculating
Figure FDA0002589799130000027
Value is then according to
Figure FDA0002589799130000028
The value avg is calculated as follows:
Figure FDA0002589799130000029
approximate A matrix and b vector as
Figure FDA00025897991300000210
Matrix sum
Figure FDA00025897991300000211
Vector, then there are:
Figure FDA00025897991300000212
wherein v, m ∈ N (u), avg is all
Figure FDA00025897991300000213
β is a constant controlling the scaling;
Figure FDA00025897991300000214
wherein v, m ∈ N (u); avg is all
Figure FDA00025897991300000215
β is a constant controlling the scaling;
Figure FDA00025897991300000216
matrix sum
Figure FDA00025897991300000217
The vectors are approximations of the A matrix and the b vector respectively, and the expression of the optimal interpolation weight is optimized as shown in the following formula:
Figure FDA00025897991300000218
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