CN107563135A - A kind of optimum structure equation model automatic generation method - Google Patents
A kind of optimum structure equation model automatic generation method Download PDFInfo
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Abstract
The present invention provides a kind of optimum structure equation model automatic generation method.The measurement model of structural equation model is being set, and on the premise of one data matrix of offer, this method goes out optimal structural model using the method intelligence computation based on global search.All measurement models and structural model are combined into full model, all optimum structure equation full models are filtered out by fit indices fit.The present invention simultaneously need not shift to an earlier date the structural model of setting structure equation model, in the case where not knowing structural model, can rapidly generate all structural models using the method, optimal structural equation model is then obtained according to fit indices degree of fitting.
Description
Technical field
The present invention relates generally to the field of computer analyzing and processing structural equation model, and in particular to a kind of optimum structure side
Journey model automatic forming method.
Background technology
Structural equation model is a kind of very general, main linear statistical modeling technique, be widely used in psychology,
The research in the fields such as economics, sociology, behavior science.In the research in these grade fields, researcher often encounters research
In the variable that is related to can not accurately and directly measure.This variable we term it latent variable, such as intelligence, learning motivation,
Family social economic status, customer satisfaction, customer loyalty etc..These latent variables can not direct accurate measurement, but can
To go to estimate it by some indirect means, i.e., go to measure those latent variables using some observation indexs.For example, learned in research
During the problem of in terms of raw scholastic achievement, researcher can be gone using the section such as Chinese language, mathematics, foreign language of student purpose achievement as
The index of student's scholastic achievement.Traditional statistical analysis technique can not handle these latent variables well, and equation of structure mould
Type just can handle these latent variables and its index well simultaneously.Comparatively, structural equation model is one very wide comprising face
Mathematical modeling, it can analyze some extremely complex relations for being related to latent variable.
Existing Structural Equation Modeling Analysis method, from the angle of application person, researcher is required for according to application field
Theoretical or experience, a basic structural equation model is proposed, then utilizes statistical analysis software, the fitting journey of computation model
Degree, the deficiency of analysis model, then manual correction model.Model still can not be fitted after Modifying model, or lose theoretical meaning
In the case of justice, or even need to re-establish model.This process needs researcher to have certain profession basis, and needs
Substantial amounts of confirmatory experiment repeatedly, wastes time and energy, allows Many researchers to hang back.With the application of structural equation model
Gradually expand, the researcher in more and more fields is desirable with structural equation model and carries out statistical analysis.Optimum structure equation mould
Type automatic generation method will be helpful to solve the problems, such as that user uses structural equation model.
The content of the invention
The present invention is directed to the deficiency of current structure equation model modeling technique, there is provided a kind of optimum structure equation model is certainly
Dynamic generation method.It is an object of the invention in the case where only determining the measurement model of structural equation model, rapidly generate
All structural models, structural equation model score is then judged according to the fit solution of fit indices, and obtain highest scoring
N number of model, concrete technical scheme is as follows.
Optimum structure equation model automatic generation method, comprises the following steps：
(a) default measurement model is stored；
(b) according to the measurement model scale of step (a), structural model all in global space is traveled through, chooses a kind of knot every time
Structure model, and combine the measurement model of step (a), equation of structure full model corresponding to structure；
(c) using the equation of structure full model in step (b) as input, parameter is estimated using Maximum Likelihood Estimation Method, and calculate
Go out the fit indices of the model；
(d) circulate operation step (b) and (c), until the structural model searched in global space；To every in ergodic process
Individual structural model scoring；
(e) receive scope, computation model score according to fit indices, and sorted according to score height, preserve the knot of highest scoring
Structure equation full model.
Above-mentioned optimum structure equation model automatic generation method, in step (a), using specific data structure storage organization side
On the full model of journey, including all observational variables in model, all latent variables, variable attaching relation and each attaching relation
Factor load capacity.The data structure of design includes three attributes：1 observational variable list, 1 latent variable list, and one
Individual two-dimensional matrix.Wherein the line number of two-dimensional matrix is the quantity of latent variable, and columns is total of observational variable and latent variable
Number.
Above-mentioned optimum structure equation model automatic generation method, in step (b), devise specific traversal method.The party
Method according to the quantity m of the latent variable of structural equation model to be analyzed, calculates the overall situation being made up of all structural relations first
Space size N, wherein N=3m(m-1)/2.Then one in corresponding global space is represented using 0 ~ N-1 ternary representation
Kind structural relation.Such as the number of hypothesis latent variable is 3, then the size of global space is N=33(3-1)/2=27.Use 0 ~ 26
Ternary form of presentation of one of numeral represents a kind of relation of global variable, i.e. the 1st kind of structural relation is 000(3),
2nd kind of structural relation is 001(3)... the 27th kind of structural relation is 222(3).Assuming that above latent variable form digraph for G=<
V,E>, V={ v1, v2, v3 }, the numeral ' 0 ' of trit represents that side is not present, and ' 1 ' represents positive side be present, and ' 2 ' represent reversely
Side, i.e., ' 011 ' represents that relation, v1 → v3, v2 → v3 is not present between v1v2.By that analogy.After structural relation is determined, relation
Form according to the adjacency matrix of digraph 01 is stored in the data structure of (a) design.
Above-mentioned optimum structure equation model automatic generation method, it is characterised in that the data structure conversion in (a) is devised in (c)
For the method for the structural equation model Construction of A Model sentence in R language.Structural equation model to be analyzed, it is to use R language sem
What the structural equation model definition statement in software kit defined.The data conversion of data structure in (a) into model definition language,
R Language Processings are transmitted to, and estimation parameter and fit indices are drawn using Maximum Likelihood Estimation Method.
Above-mentioned optimum structure equation model automatic generation method, it is characterised in that in (e), devise a kind of equation of structure mould
Type methods of marking.According to pre-set measurement model, structural model and data matrix, a series of fittings can be calculated and referred to
Numerical value.This method utilizes the fit indices value of structural equation model, is given a mark for structural equation model.Specific marking mode is,
The score of the model is equal to the summation of the fit indices number for the range of fit for meeting fit indices.The fitting of i.e. one model refers to
In number, there are more fit indices to meet and receive scope, model score is higher.For example, it is assumed that given a mark according to 10 fit indices, such as
The value that fruit has 8 fit indices is to meet the range of fit of the fit indices, then makes 8 scores to the model.
Above-mentioned optimum structure equation model automatic generation method, it is characterised in that devised in (e) and filter out optimal knot
The screening technique of structure equation full model.This method is the score of structural equation model as key, and score is higher, and model is better.Cause
This come storage organization equation model, initially sets up the heap that size is N, N is optimum structure equation model using the structure of most rickle
Number, every time be passed to a structural equation model, if the score of model is lower than the score of root node, discard the model；Phase
If the score of the anti-model is higher than root node, root node is rejected, the model is injected in heap and builds heap again.It is defeated always
Enter until all structural equation models of global space all travel through one time, it is optimal N number of model to obtain N number of model in heap.
Compared with prior art, the invention has the advantages that and technique effect：
Present Structural Equation Modeling Analysis method, from the angle of application person, it is required for theory of the researcher according to application field
Or experience, a structural equation model comprising measurement model and structural model is proposed, then utilizes statistical analysis software, meter
Calculate the fitting degree of model, the deficiency of analysis model, then manual correction model.Model still can not be fitted after Modifying model,
Or in the case of losing theory significance, or even need to re-establish model.This process needs researcher to have necessarily special
Industry basis, and substantial amounts of confirmatory experiment repeatedly is needed, waste time and energy, allow Many researchers to hang back.The present invention is simultaneously not required to
Shift to an earlier date the structural model of setting structure equation model, in the case where not knowing structural model, the method can be utilized rapid
All structural models of generation, then application person optimal equation of structure mould can be obtained according to fit indices interested
Type.
Brief description of the drawings
Fig. 1 is the observational variable of two-dimensional matrix and the attaching relation schematic diagram of latent variable in embodiment.
Fig. 2 is the flow chart of optimum structure equation model automatic generation method in embodiment.
Embodiment
Embodiments of the present invention are described further below in conjunction with accompanying drawing, but the implementation not limited to this of the present invention, need
, it is noted that if following have not the especially process for detaileds description, be those skilled in the art can refer to prior art realization or
Understand.
Such as Fig. 2, the main flow of optimum structure equation model automatic generation method comprises the following steps：
(a) measurement model that user is set, data file are read in；
(b) model storage is measured；
(c) all structural models in search space, and digital simulation index；
(d) score is calculated to all models, and is sorted according to score height；
(e) optimal all models are preserved.
Step (a) allows user to set measurement model by web interface, including sets all observational variables, all potential
Factor load capacity on variable, variable attaching relation and each attaching relation.Uploaded format is Excel data file simultaneously,
It is required that the data in the data file have specific form.State optimum structure equation model automatic generation method, in step (a),
Using the full model of specific data structure storage organization equation, including all observational variables in model, all latent variables, change
Measure the factor load capacity on attaching relation and each attaching relation.The data structure of design includes three attributes：1 observational variable
List, 1 latent variable list, and a two-dimensional matrix.Wherein the line number of two-dimensional matrix is the quantity of latent variable, and columns is
The total number of observational variable and latent variable.As shown in Figure 1.The 01 of the digraph that wherein left-half is formed between latent variable
Adjacency matrix, right half part represent the attaching relation between latent variable and observational variable.In right half part, the element value of matrix
AijRepresent and attaching relation between latent variable i and observational variable j be present, and immobilisation factor load capacity is value Aij.If element value Aij
Represented for " -9999 " and attaching relation between latent variable i and observational variable j be present, but factor load capacity is to be estimated.If element value
AijValue is not deposited, then represents and attaching relation is not present between latent variable i and observational variable j.
Step (b) is using the structure storage measurement model of matrix, and the row representative of matrix is latent variable, and line number is equal to latent
In the number of variable.What matrix column represented is that latent variable and observation variable, columns etc. add observation with latent variable number
The number of variable.The first half element representative structure model of matrix, latter half represents measurement model, with specific element value
To represent attaching relation and structural relation.Above-mentioned optimum structure equation model automatic generation method, in step (b), devise spy
Fixed traversal method.This method according to the quantity m of the latent variable of structural equation model to be analyzed, is calculated by all knots first
The global space size N that structure relation is formed, wherein N=3m(m-1)/2.Then represented pair using 0 ~ N-1 ternary representation
Answer a kind of structural relation in global space.Such as the number of hypothesis latent variable is 3, then the size of global space is N=33(3 -1)/2=27.A kind of relation of global variable, i.e., the 1st kind are represented using the ternary form of presentation of 0 ~ 26 one of numeral
Structural relation is 000(3), the 2nd kind of structural relation is 001(3)... the 27th kind of structural relation is 222(3).Assuming that above latent variable
The digraph of composition be G=<V,E>, V={ v1, v2, v3 }, the numeral ' 0 ' of trit represents that side is not present, and ' 1 ' represents presence
Positive side, ' 2 ' represent reverse edge, i.e., relation, v1 → v3, v2 → v3 is not present between ' 011 ' expression v1v2.By that analogy.It is determined that
After structural relation, relation is stored in the data structure of (a) design according to the form of the adjacency matrix of digraph 01.
The method that step (c) uses exhaustive search, include all structures corresponding to the measurement model set in step (b)
Model, and using them as complete full model, analyzed one by one.Using the sem program bags in R language, using greatly seemingly
Right method of estimation, all parameter values to be estimated of appraising model, and thus calculate fit indices.Such as the survey set in user
Measure in model, the number of latent variable is n, and the relation between each two latent variable there are 3 kinds, then the model has n (n-1)/2
Different latent variables pair.Then the size of global space is 3 n (n-1)/2 power.Search for what the structural model of global space referred to
It is 0 to 3 n (n-1)/2 power to be converted to represent a kind of character string of structural relation respectively.Built further according to the structural relation
Equation of structure full model.
Model score is that the number for the number for receiving scope for meeting fit indices according to the model calculates in step (d)
's.In the fit indices of one model, there are more fit indices to meet and receive scope, model score is higher.Use special number
Model is sorted according to structure storage model, and according to model score, n model for obtaining highest scoring is n optimal mould
Type.
As above it can preferably realize the present invention and obtain the technique effect.The present invention simultaneously need not shift to an earlier date setting structure
The structural model of equation model, in the case where not knowing structural model, it can rapidly generate all structures using the method
Model, then application person optimal structural equation model can be obtained according to fit indices interested.
Claims (6)
1. a kind of optimum structure equation model automatic generation method, it is characterised in that comprise the following steps：
(a) default measurement model is stored；
(b) according to the measurement model scale of step (a), structural model all in global space is traveled through, chooses a kind of knot every time
Structure model, and combine the measurement model of step (a), equation of structure full model corresponding to structure；
(c) using the equation of structure full model in step (b) as input, parameter is estimated using Maximum Likelihood Estimation Method, and calculate
Go out the fit indices of the model；
(d) circulate operation step (b) and (c), until the structural model searched in global space；To every in ergodic process
Individual structural model scoring；
(e) receive scope, computation model score according to fit indices, and sorted according to score height, preserve the knot of highest scoring
Structure equation full model.
2. optimum structure equation model automatic generation method according to claim 1, it is characterised in that in step (a), use
The full model of the data structure storage equation of structure is set, including all observational variables, all latent variables, variable in model is returned
Factor load capacity in category relation and each attaching relation；The data structure of setting includes three attributes：Observational variable list is dived
In variable list and a two-dimensional matrix；Wherein the line number of two-dimensional matrix be latent variable quantity, columns be observational variable and
The total number of latent variable.
3. optimum structure equation model automatic generation method according to claim 2, it is characterised in that in step (b), first
According to the quantity m of the latent variable of structural equation model to be analyzed, it is big to calculate the global space being made up of all structural relations
Small N, wherein N=3m(m-1)/2；Then a kind of structure in corresponding global space is represented using 0 ~ N-1 ternary representation
Relation；After structural relation is determined, relation is stored according to the form of 01 adjacency matrix of digraph the number of step (a) setting
According in structure.
4. optimum structure equation model automatic generation method according to claim 1, it is characterised in that in step (c), treat point
The structural equation model of analysis, defined using the structural equation model definition statement in R language sem software kits；Step (a)
The data conversion of middle data structure is transmitted to R Language Processings, and draw estimation using Maximum Likelihood Estimation Method into model definition language
Parameter and fit indices.
5. optimum structure equation model automatic generation method according to claim 1, it is characterised in that in step (d), according to
Pre-set measurement model, structural model and data matrix, calculate a series of fit indices values；Utilize equation of structure mould
The fit indices value of type, given a mark for structural equation model, specific marking mode, which is that the score of corresponding model is equal to, meets fitting
The summation of the fit indices number of the range of fit of index, i.e., in the fit indices of one model, there are more fit indices to meet
Receive scope, model score is higher.
6. optimum structure equation model automatic generation method according to claim 1, it is characterised in that in step (e), knot
The score of structure equation model is as key, and score is higher, and model is better；Using the structure of most rickle come storage organization equation model,
The heap that size is N is initially set up, N is the number of optimum structure equation model, a structural equation model is passed to every time, if model
Score it is lower than the score of root node, discard the model；If the score of the opposite model is higher than root node, root section is rejected
Point, the model is injected in heap and builds heap again；Input always until all structural equation models of global space all travel through
One time, it is optimal N number of model to obtain N number of model in heap.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110853679A (en) * | 2019-10-23 | 2020-02-28 | 百度在线网络技术（北京）有限公司 | Speech synthesis evaluation method and device, electronic equipment and readable storage medium |
| CN112559848A (en) * | 2020-12-14 | 2021-03-26 | 华南理工大学 | Manifold searching method of optimal weighted directed graph |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110853679A (en) * | 2019-10-23 | 2020-02-28 | 百度在线网络技术（北京）有限公司 | Speech synthesis evaluation method and device, electronic equipment and readable storage medium |
| CN110853679B (en) * | 2019-10-23 | 2022-06-28 | 百度在线网络技术（北京）有限公司 | Speech synthesis evaluation method and device, electronic equipment and readable storage medium |
| CN112559848A (en) * | 2020-12-14 | 2021-03-26 | 华南理工大学 | Manifold searching method of optimal weighted directed graph |
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