KR102282982B1 - Apparatus and method for providing multi-level model interface - Google Patents

Abstract

The method for providing a multi-layer model interface performed by an information processing apparatus according to an embodiment of the present invention includes the steps of receiving analysis data to be analyzed through the input unit, and receiving a dependent variable for regression analysis based on the analysis data. , displaying, by the processor, a visualized tree model including an intercept coefficient of a first level for describing the dependent variable and a first error term of a first level for the dependent variable through the display unit, and through the input unit receiving a first explanatory variable of a first level describing the dependent variable, and displaying, by the processor, adding the first explanatory variable of the first level to the visualized tree model.

Description

Apparatus and method for providing multi-level model interface

The present invention relates to an apparatus and method for providing a multilayer model interface.

The multi-layered model is a methodologically appropriate statistical model for the analysis of hierarchical data. Since its publication in the academic community in the mid-1980s (Aitkin & Longford, 1986; Raudenbush & Bryk, 1986; Goldstein & Rasbash, 1986), it has been widely used in pedagogical research. It has been used as a universal statistical model in all academic fields.

A statistical model is a mathematical model that properly reflects the structure of data and at the same time reflects the researcher's theory. Traditional statistical models have limitations in that the model cannot reflect the hierarchical characteristics of data. The multi-layer model reflects the hierarchical characteristics of data, and is a statistical model suitable for multi-layer data analysis, and new multi-layer models are continuously being developed.

Korean Patent Publication No. 10-2019-0015949 (published)

The multi-layered model interface providing apparatus and method according to an embodiment of the present invention for solving the above-mentioned conventional problems avoids the mathematical complexity of the multi-layered model and helps researchers to understand the concept of the model in a limited space of the window screen. By specifying the multi-layered model with figures that include all of the fixed-effect parameters, random-effect parameters, dependent and independent variables, the purpose is to enable users to visually accurately and easily understand the features of multi-layered models through the model conceptual diagram. do it with

An input unit for receiving information input from a user according to an embodiment of the present invention for achieving the above object, a processor for generating a signal to display a multi-layered model on the screen based on the input information, and receiving the signal The method for providing a multi-layer model interface performed in an information processing apparatus including a display unit for providing the multi-layer model as the screen includes the steps of: receiving analysis data to be analyzed through the input unit; regression analysis based on the analysis data; receiving, by the processor, a first-level intercept coefficient for explaining the dependent variable, and displaying a visualized tree model including a first-level first error term for the dependent variable through the display unit and receiving a first explanatory variable of a first level describing the dependent variable through the input unit, and displaying, by the processor, adding the first explanatory variable of the first level to the visualized tree model can do.

In addition, an apparatus for providing a multi-layer model interface according to another embodiment of the present invention for achieving the above object includes an input unit for receiving information input from a user, and a signal to display a multi-layer model on a screen based on the input information A processor for generating a , and a display unit receiving the signal generated from the processor and providing the multi-layered model as the screen; the processor comprising: receiving analysis data to be analyzed through the input unit; receiving a dependent variable for regression analysis based on the analysis data; displaying, by the processor, a visualized tree model including an intercept coefficient of a first level for describing the dependent variable and a first error term of a first level for the dependent variable through the display unit; and receiving a first explanatory variable of a first level describing the dependent variable through the input unit, and adding and displaying, by the processor, the first explanatory variable of the first level to the visualized tree model. can

In addition, the present invention proposes a computer program stored in a computer-readable recording medium for executing the method for providing a multi-layer model interface according to the above method.

The apparatus and method for providing a multilayer model interface according to an embodiment of the present invention can avoid the mathematical complexity of the multilayer model and specify and express even a complex statistical model in the limited space of the window screen in order to help the researcher's conceptual understanding of the model. They have the effect of being able to easily understand the structural characteristics and mathematical complexity of multi-layered models visually through the conceptual diagram.

1 is a flowchart schematically illustrating an apparatus and method for providing a multi-layered model according to an embodiment of the present invention over time.
FIG. 2 is a more detailed flowchart of the detailed steps of FIG. 1 .
3 is a diagram for explaining the name of a multi-layer model and a model for each level that is a part of the multi-layer model according to an embodiment of the present invention.
4 is a diagram illustrating a two-level multi-layer model according to an embodiment of the present invention.
5 is a view showing a linear growth model basic model and a non-linear growth model basic model according to an embodiment of the present invention.
6 is a diagram exemplarily showing a basic model specification screen of a 2-level multi-layered model according to an embodiment of the present invention.
7 is a diagram illustrating a specification process of a research model of a two-level multilayer model according to an embodiment of the present invention.
8 is a diagram illustrating a method of specifying a basic model and a research model of a linear multi-layer growth model according to an embodiment of the present invention.
9 is a conceptual diagram illustrating a three-level multi-layer model according to an embodiment of the present invention.
10 is a diagram illustrating a process of specifying a three-level model according to an embodiment of the present invention.
11 is a diagram illustrating a basic model and a research model of a cross-classification multi-layered model according to an embodiment of the present invention.
12 is a block diagram schematically illustrating the configuration of an apparatus for providing a multilayer model interface according to an embodiment of the present invention.

Hereinafter, the present invention will be described in detail by describing preferred embodiments of the present invention with reference to the accompanying drawings. However, the present invention may be embodied in several different forms.

and is not limited to the described embodiment. In addition, in order to clearly explain the present invention, parts irrelevant to the description are omitted, and the same reference numerals in the drawings indicate the same members. Throughout the specification, when a part "includes" a certain component, this does not exclude other components unless otherwise stated, but means that other components may be further included. In addition, terms such as "...unit", "...group", "module", and "block" described in the specification mean a unit that processes at least one function or operation, which is hardware, software, or hardware. and a combination of software. Hereinafter, an embodiment of the present invention will be described in detail with reference to the accompanying drawings. In addition, in describing the present invention, if it is determined that a detailed description of a related known configuration or function may obscure the gist of the present invention, the detailed description may be omitted.

Hereinafter, an apparatus and method for providing a multi-layer model interface performed in an information processing apparatus having a user interface according to an embodiment of the present invention will be described in detail with reference to the drawings below.

The apparatus for providing a multi-layer model interface according to an embodiment of the present invention is an information processing apparatus having a user interface, and may be performed based on a multi-level modeling (MLM) multi-layer model computer program (hereinafter referred to as an MLM program (tentative name)). That is, the user can statistically analyze the data to be processed using the multi-layer model interface providing method of the present invention, which is performed based on the MLM program through the user interface.

Such an MLM program is a program that can analyze data by a 2-level multilevel model, a 3-level multilevel model, and a 2-level cross-classified multilevel model. Data analysis may also be included. The 2-level and 3-level multi-layer models are multi-layer models that have a standard function among the many newly developed multi-layer models, and the cross-classification multi-layer model is a model in the area where new models are being developed recently. Therefore, the MLM program can be said to be a program that supports standard models among existing multi-layered models. The MLM program can consist of three modules: MLM2 module, MLM3 module, and CMLM module. Specifically, MLM2 module (hereinafter referred to as MLM2) is a 2-level multi-layered model program, and MLM3 module (hereinafter referred to as MLM3) is a 3 -Level Multilevel Model, and CMLM Module (hereafter CMLM) is a cross-classified multilevel model program.

In other words, the multilayer model interface providing apparatus of the present invention enables the specification of a 2-level multilayer model, a 3-level multilayer model, and a cross-classification multilayer model and a generalized multilayer model to be expressed in a limited single window screen according to the configuration of the MLM program. do.

The multi-layer model interface providing apparatus of the present invention avoids the mathematical complexity of the multi-layer model and presents the mathematical expression of the multi-layer model in the form of a multi-level regression model in order to help the researcher's conceptual understanding of the model, The concept of the multilayer regression model is also applied to the device that expresses the multilayer model as a picture. That is, the multi-layer model interface providing apparatus of the present invention enables users to visually accurately and easily understand the features of the multi-layer model through the model conceptual diagram. And, in the MLM program, the work of specifying the model by the user is all done in the model conceptual diagram.

Accordingly, users can use the multi-layer model interface providing device of the present invention based on the MLM program to ensure that the mathematical notation of the multi-layer model, the expression of the model conceptual diagram, and the operation of the program by the model conceptual diagram are consistent in the perspective of the multi-layer regression model. It allows for more accurate and convenient data analysis with a multi-layered model.

In the multi-layered model, models for each level are combined to form a single statistical model. Here, when referring to the multi-layered model as an overall model and the model for each level that is a part of the multi-layered model, the expression shown in FIG. 3 is used.

In other words, when expressing the entire model, the expression 'multi-layer' is used as in the '2-level multi-layer model', and when referring to the model for each level, the word 'multi-layer' is not used. Hereinafter, descriptions of the two-level multi-layer model and the three-level multi-layer model are well known, and thus descriptions thereof will be omitted.

1 is a flowchart schematically illustrating a method of providing a multilayer model interface performed in an apparatus (information processing device) for providing a multilayer model interface according to an embodiment of the present invention, and FIG. 2 is a detailed step of FIG. This is a more detailed flow chart. And, FIG. 1A is a flowchart schematically illustrating a method of providing an interface of a two-level multi-layer model, and FIG. 1B is a flowchart schematically illustrating a method of providing an interface of a three-level multi-layer model.

As shown in FIG. 12, the apparatus 100 for providing a multi-layer model interface of the present invention includes an input unit 110 for receiving information input from a user, and a signal to display a multi-layer model on the screen based on the input information. It may be configured to include a processor 120 that generates, and a display unit 130 that receives the signal and provides a multi-layered model as a screen.

Referring to FIG. 1A , the input unit of the apparatus for providing a multilayer model interface according to an embodiment of the present invention first selects a type of multilayer model (eg, a longitudinal model or a cross-section model) to be used by the user through the user interface in step S100. As a result, the type of the multi-layer model and the group ID are inputted. In the 2-level multi-layer model, only one group ID is input, and in the 3-level multi-layer model, two IDs are input: a 2-level group ID and a 3-level group ID. In the case of a cross-classification multi-layer model, the row group ID and column group ID are input.

In addition, the input unit receives a dependent variable for regression analysis in step S200. Accordingly, in step S300, the processor displays the intercept coefficient of the first level for the input dependent variable and displays the error term, and the input unit receives information about the first intercept coefficient and the error term of the first level from the user. .

The display unit of the present invention configures the dependent variable as described above and the variables of the first level accordingly in a visualized tree model, and in step S400, the processor uses the display unit to describe the intercept coefficient of the first level through the display unit. The first intercept coefficient of the second level using the intercept coefficient as a dependent variable and the first error term of the first level with respect to the intercept coefficient of the first level may be added to the visualized tree model and displayed.

If there is a variable to be additionally added during the modeling process of the first level and the second level in steps S300 to S400 above, it can be displayed by adding it to the tree model in the same way as above. In step S500, if the model configuration of the displayed tree model is completed according to the operation sequence as described above, the equation corresponding to the tree model may be displayed together so that the user can check it once again. If it is confirmed by the user, data analysis is performed by executing the multi-layer model in step S600.

Fig. 1b relates to a method for providing an interface of a three-level multi-layer model. The operation sequence and principle of Fig. 1a are the same, but as in S500 of Fig. 1b, coefficients for explaining the coefficients according to the second level are added to the third level. The added tree model can be displayed.

And, referring to FIG. 2a, which is a detailed flowchart between steps S300 and S400 in FIG. 1, the apparatus for providing a multi-layer model interface of the present invention provides a dependent variable according to an input from a user through a user interface in step S310, after step S300. It is checked whether the input of whether to add the first explanatory variable of the first level for

If the user inputs for adding the first explanatory variable in step S320, the processor activates the dependent variable in step S320 and displays the first explanatory variable of the first level input by the user through the display unit in step S330. Accordingly, the processor may set the centralization type for the first explanatory variable of the first level according to the centralization option input by the user in step S340 . That is, the processor may be set to one of grand mean centering, group mean centering, and no centering.

In operation S350 , the processor may display the second error term of the first level with respect to the first regression coefficient according to the first explanatory variable of the first level through the display unit. If the first regression coefficient of the first level has a radio effect, the second error term of the first level is displayed, and if the first regression coefficient has a fixed effect, the second error term of the first level is deleted. Then, in step S310 again, the process up to S350 may be repeated by checking whether an input related to the addition of another explanatory variable is input.

If the user does not input to add the first explanatory variable of the first level in step S310, the process proceeds to step S400.

FIG. 2B is a flowchart detailing the process between steps S400 and S500 in FIG. 1 . First, in step S410, if there is an input from the user for adding an explanatory variable using the intercept coefficient of the first level as a dependent variable, the processor activates the intercept coefficient of the first level in step S420 and the first level in step S430 A first explanatory variable of the second level with respect to the intercept coefficient of the level may be displayed. Then, in step S440, the processor sets the centralization option of the first explanatory variable of the second level.

Thereafter, in step S450 , it is checked whether a user input for adding an explanatory variable using the intercept coefficient of the first level as a dependent variable in addition to the first explanatory variable of the second level is checked. If there is a user input in step S450, the process returns to step S430 to perform a setting process for the second explanatory variable of another second level.

On the other hand, if there is no user input in step S450, whether there is a regression coefficient to be further explained by explaining it as a dependent variable of the 2-level model among at least one regression coefficient of the first level in step S460 is determined through the user's input. Check it. If there is a user input in step S460, the corresponding regression coefficient selected in step S470 is activated as a dependent variable, and the tree model of the two-level model for the regression coefficient of the selected first level can be further displayed by returning to step S430. do.

If there is no regression coefficient of the first level to be further described in step S460, the process proceeds to step S500.

Next, FIG. 2C is a flowchart detailing the process between steps S500 and S600 in FIG. 1B.

First, in step S510, if there is an input from the user for adding an explanatory variable using the first intercept coefficient of the second level as a dependent variable, the processor activates the first intercept coefficient of the second level in step S520, and step S530 may indicate a first explanatory variable of a third level with respect to the first intercept coefficient of the second level. Then, in step S450, the processor sets the centralization option of the first explanatory variable of the third level.

Thereafter, in step S550 , it is checked whether a user input for adding an explanatory variable having the intercept coefficient of the second level as a dependent variable in addition to the first explanatory variable of the third level is checked. If there is a user input in step S550, the process returns to step S530 to perform a setting process for the second explanatory variable of another third level.

On the other hand, if there is no user input in step S550, it is determined whether there is a regression coefficient to be further explained by explaining it as a dependent variable of the 3-level model among at least one regression coefficient of the second level in step S560 through the user's input. Check it. If there is a user's input in step S560, the corresponding regression coefficient selected in step S570 is activated as a dependent variable, and the tree model of the 3-level model for the regression coefficient of the selected second level can be further displayed by returning to step S530. do.

If there is no regression coefficient of the second level to be further described in step S560, the process proceeds to step S600.

The above description of FIGS. 1 and 2 is a brief description of the specification process according to the 2-level model and the 3-level model according to an embodiment, and the detailed description and the 3-level model, and the cross-classification multi-layer The specification method for the model will be described in more detail with reference to FIGS. 3 to 11 below.

<Equation 1> and <Equation 2> below represent a 1-level model and a 2-level model, respectively.

Here, if the SES variable is an explanatory variable (independent variable), β _0j is the intercept coefficient, and β _1j is the regression coefficient according to the SES variable in the j-th group. e _ij is an error term in each group and has a random effect. σ ² represents the variance of error within each group.

Here, γ ₀₀ , γ ₀₁ , γ ₁₀ , and γ ₁₁ are regression coefficients and are fixed effect parameters. The 2-level model can be understood as a regression model with each regression coefficient as a dependent variable. Since <Equation 2> has two dependent variables, it can be called a multivariate regression model. It is assumed that the error terms u _0j and u _1j have a multivariate normal distribution as in <Equation 2> above. where τ ₀₀ is the residual variance for the intercept coefficient in the 1-level model, and τ ₁₁ is the intergroup residual variance of the SES effect.

The above <Equation 1> to <Equation 2> are a two-level multi-layered model as one statistical model. A pictorial representation of such a two-level multilayer model is shown in FIG. 4A. Figure 4a conceptualizes the multi-layer model in the form of a multi-layer regression model. In Fig. 4a, the 1-level regression coefficient is shown as the dependent variable of the 2-level model. The multilayer model interface providing apparatus of the present invention has a system in which the researcher's analysis model is determined and implemented by selecting or changing each element constituting FIG. 4 .

The 2-level multi-layer model can be understood as a multi-layer regression model, and the 1-level and 2-level models are specified by the method of the regression model. Therefore, as with the regression model, as many explanatory variables as the data allow, each level can be included in the model.

Next, the general model of the 2-level multi-layered model will be described. Now j=1, 2, … , i=1, 2, … for each J group. ., n If a _{general 2-level multilevel model for analyzing data embedded in j} observation units (eg, people) is presented, the 1-level regression model is as follows <Equation 3> same as

)의 차이이며 무선효과를 갖고 평균은 0이며 분산은 σ²임.Here, i=1,2,… .n _j , j=1, 2, … , J, p=0, 1, 2, … , P, and the definitions of each term are as follows _{: Y ij} : the value of the dependent variable Y of the i-th observation unit (or person, hereinafter, observation unit) _{belonging to the j-th group, X pij} : the i-th observation unit belonging to the j-th group of the p-th explanatory variable (X _p ), β _pj : the regression coefficient for the dependent variable of the p-th explanatory variable (X _{p ) in the j-th group, e ij} : the residual term, the actual value of the _{dependent variable Y ij and the regression line (}

), has a random effect, the mean is 0, and the variance is σ ² .

Since each regression coefficient, β _pj in <Equation 3> may be different for each j group, a 2-level regression model using (P+1) each regression coefficient β _{pj as a dependent variable is} can be expressed together.

where q=0, 1, 2, ... .Q _p , and γ _pq : the regression coefficient for _{β pj} of the q-th 2-level explanatory variable. Therefore, the combination of 2-level explanatory variables _{may be different for each β pj} (p=0, 1, 2, …P) 1-level regression coefficient. And, W _qj is the q-th 2-level explanatory variable, and u _pj is the 2-level radio effect error term.

, T)이 다변량 분포를 가지며, T는 (P+1)X(P+1) 차원의 분산-공분산 행렬이다.Since the 2-level model has (P+1) dependent variables, (P+1) u _pj have mean, variance and covariance. The mean of each u _pj is 0, and the variance is Var(u _pj )=τ _pp' . Therefore, the two-level error term is MN(

, T) has a multivariate distribution, and T is a variance-covariance matrix of dimension (P+1)X(P+1).

In the 2-level multi-layer model, the error term u _pj of the 2-level model can be ignored or significantly reflected in the model depending on the intention of the researcher. There are four ways to deal with the error term upj in the 2-level model.

① β _pj = γ _p0 : This model assumes that the 1-level regression coefficient β _pj is the same for all groups. That is, _{the effect of the X p} variable on Y _ij is the regression coefficient γ _p0 .

② β _pj = τ _p0 + u _pj : This is a model that assumes that the 1-level regression coefficient β _{pj is different for each group.} u _pj is the effect of the jth group.

: 1-수준 회귀계수 β_pj가 집단에 따라 다르지만 Q_p개의 2-수준 설명변수로 β_pj의 변산을 온전히 설명한다고 가정한 모형이다.③ β _pj = τ _p0 +

: This model assumes that although the 1-level regression coefficient β _pj varies depending on the group, Q _p 2-level explanatory variables fully explain the variability of _{β pj.}

+ u_pj: 1-수준 회귀계수 β_pj가 집단에 따라 다르며 Q_p개의 2-수준 설명변수로 β_pj의 변산을 설명한 이후에도 여전히 잔차 변산이 남아있다고 가정한 모형이다.④ β _pj = τ _p0 +

+ u _pj : This is a model that assumes that the 1-level regression coefficient β _pj varies according to the group, and that residual variability still remains after the variability of _{β pj is explained with Q p} 2-level explanatory variables.

Therefore, users can treat the 1-level regression coefficient β _pj as a fixed effect parameter as in ① and ③, or assume it as a regression coefficient with a random effect as in ② and ④.

If the above <Equation 3> and <Equation 4> are expressed as a figure, it is as shown in Figure 4b.

Figure 4b shows how a multilayer model can be conceptualized in the form of a multilayer regression model. A regression model is basically a mathematical model expressing the structural relationship between multiple explanatory variables and one dependent variable. Figure 4b considers the increase in the number of explanatory variables in the 2-level, and the apparatus for providing a multi-layer model interface of the present invention sets each component of Figure 4b to determine the user's analysis model.

Next, a two-level multi-layered growth model will be described. The 2-level multi-layer model for analyzing longitudinal data is mathematically the same as the multi-layer model for analyzing cross-sectional data. However, since the situation in which the model is applied is different, the model and the notation are different.

The 2-level multi-layered growth model includes a basic model and a research model. The growth trajectory of each individual of the dependent variable is highly likely to have linearity. If the number of repeated observations or the observation period is long, it is highly likely to appear as a nonlinear curve. The following <Equation 5> and <Equation 6> show the basic model of the linear growth model and the basic model of the non-linear growth model, respectively.

Both models such as <Equation 5> and <Equation 6> _{include only the time variable (A ti} ) in the 1-level model, and distribution information of the _{1-level regression coefficient π pi in the 2-level model.} Here, the 1-level model is a submodel of the multi-order model, which is a general growth curve model. 5A and 5B show <Equation 5> and <Equation 6>.

The research model of the multi-layered growth model is a model that explains the variation of change parameters by adding explanatory variables to the 2-level model of the basic model. In other words, the 1-level model of the basic model is maintained as it is and the model explains the _{variation of the change parameter π pi .} The following <Equation 7> shows an example of a research model.

Since the multi-layer growth model is the same statistical model as the multi-layer model for cross-sectional data analysis, the model concept can also be expressed in the same way. 5c shows the above <Equation 7>.

Next, the specification method according to the case where the 2-level multi-layer data is cross-sectional data is described. More specifically, the method of specifying the basic model, the Ancova model, and the random effect regression model in 2-level cross-sectional data, and the procedure for performing data analysis in the MLM program according to the various models as described above are outlined. .

First, the procedure for performing data analysis using the MLM program is largely divided into the program module selection step (step 1), model specification in the model conceptual diagram (step 2), and analysis execution and result file storage step (step 3). is divided into

If the tasks performed in one window through the user interface are more specific, in the first step, data import, program module selection (MLM2, MLM3, CMLM selection), and analysis type selection (cross-sectional model, vertical model selection) are available. In the second stage, there are two-level ID variable selection, dependent variable selection, and model specification work in the model conceptual diagram, and in the third stage there are analysis execution and result file saving.

Here, the basic model specification step according to an embodiment of the present invention will be described. 6 is a diagram illustrating an exemplary basic model specification screen.

Figure 6a is a view showing the loading of data to be analyzed statistically on the window screen, Figure 6b is a view showing the analysis type selection step, Figure 6c is a cross-model, selecting a group ID and selecting a dependent variable A diagram showing the steps. The multilayer model interface providing apparatus of the present invention specifies the basic model as shown in FIG. 6D through the process of FIGS. 6A to 6C in this way. In Fig. 6d, Y _ij denotes the explanatory variable as the dependent variable, β _0j denotes the first intercept coefficient of the first level, which is the _{random effect intercept coefficient of the 1-level model, and γ 00} denotes the fixed effect intercept of the 2-level model. The first intercept coefficient of the second level, which is a coefficient, is indicated, and the small circles (e _ij , u _{0j ) above the dependent variable Y ij} and the intercept coefficient β _0j indicate the error terms at each level.

In the case of the basic model, if the group ID and the dependent variable are described as above, they are immediately generated, so the analysis can be performed immediately in the step of FIG. 6d.

Next, with reference to FIG. 7, the specification process of the research model (Ancova model) will be described. 7A is a process of inputting variables into the 1-level model according to the research model. In the same state as in FIG. 7A, if you right-click the name of a variable you want to input into the 1-level model in the left pane of the screen, three kinds of centering (centering) are performed. ) option appears. If you right-click on the variable 'father education', which is an embodiment, a screen as shown in FIG. 7B appears. If the user clicks the desired centering method among the three options, the variable is input to the 1-level model accordingly. For example, [No Centering] is an option for no centering, [Group mean Centering] is for centering the group mean, and [Grand mean Centering] is an option for centering the overall mean.

In this embodiment, specifying the model using the [No Centering] option will be described later. 7C shows a circle _{of u 1j} , which is the second error term of the first level, for the variable when a variable (the first regression coefficient for the first explanatory variable of the first level) is input in the one-level model. In other words, in MLM2, when a 1-level variable is input, the default condition is that the corresponding regression coefficient has a 2-level radio effect. Depending on the model set by the user, the 2-level radio effect can be canceled. there is. One example, the 'father Education' of the first level corresponding to a variable when you do not want to specify a two-level radio effect of the first regression coefficient (β _1j) Click the circle u _1j (the error term), and the β _1j If you want to reassign the 2-level radio effect, just click the circle of _{u 1j again.}

If you want to delete a 1-level variable (β _1j ) during model specification, right-click the regression coefficient of _{the variable (β 1j ) you want to delete.} If you right-click, the 'Delete' window appears, and if you click 'Delete', the variable is deleted.

If the 1-level model specification is completed and a variable is added to the 2-level model, the first intercept coefficient (β _0j ) of the first level is treated as a dependent variable as shown in Fig. 7d, and the regression coefficient of the 2-level model is treated as a dependent variable. Click (Dependent Variable). When this is clicked, the regression coefficient of the 2-level model, which is the first intercept coefficient of the first level, is activated while the circle shown in FIG. In the state shown in FIG. 7D, if you right-click the name of a variable you want to define additionally in the 2-level model in the left pane of the screen, two centering options are presented. If the user clicks on the desired option among the two centralization methods, the two-level model is input accordingly. If you do not want to center the variables, select [No Centering], and if you want to center the overall mean, select [Grand mean Centering].

Fig. 7e is a screen that appears when [No Centering] is selected in Fig. 7d, and Fig. 7f shows the model specification step of the 2-level intercept coefficient, in which variables for 'low income class ratio' and 'teacher morale rating' are added. shows That is, in the 1-level model, the 'father's education' variable (the first explanatory variable of the first level) is added, and in the 2-level model, the intercept (the first intercept coefficient of the first level) and the regression coefficient (the first level of the first level model) are added. It is a model in which two school-level variables (explanatory variables at the third level) are added to the first regression coefficient), respectively, and it is a model conceptual diagram specifying that the regression coefficient of 'father education' has a fixed effect.

_{At this time, if you click and activate the circle of u 1j} , which is the error term of the first regression coefficient of the first level, which is the 'father education' regression coefficient, a multi-layered model with a random effect of the regression coefficient in the 2-level model is specified. <Equation 8> represents the multi-layer model equation corresponding to the multi-layer model conceptual diagram presented as shown in FIG. 7F.

Next, a basic model specification method of the linear multilayer growth model will be schematically described with reference to FIG. 8 . First, when the user wants to specify the longitudinal model, the user calls the data in the same way as the transverse model specification method, and selects the longitudinal model on the screen as shown in FIG. 6B . Then, the dependent variable to be specified is selected. In the case of the cross-sectional model, the schematic presented immediately after the selection of the dependent variable is the basic model, but the longitudinal model is to report the rate of change of the dependent variable with the passage of time. should be added Accordingly, the dependent variable is activated by clicking the circle of the _{dependent variable (Y ij} ) as shown in FIG. 8A .

When the dependent variable circle is activated and the name of the time variable (Time) is clicked on the left pane of the screen as shown in Fig. 8b, three centering options appear. The three centralization options have the same meaning and function as the centralization options described in the cross-model specification step. The longitudinal model has the purpose of estimating the parameter of the initial time point and the parameter of the rate of change with time, and illuminating the relationship between the two. For example, in the MLM program of the present invention, the coding of the time variable in the longitudinal model specification step may be sequentially coded as “0” at the initial time point and “1, 2, 3, 4” according to the time interval. In Fig. 8c according to an embodiment, since it is exemplified that the time variable is coded as described above, [No Centering] is selected. When the time variable is added, the specification of the basic model of the linear multi-layered growth model (longitudinal model) is completed. <Equation 9> is a conceptual diagram showing the basic model of the linear multi-layer growth model as shown in FIG. 8D.

Here, Y _ij is the dependent variable, π _0j is the initial time point parameter for each individual in the 1-level model and is the _{random effect, and π 1j is the individual rate of change parameter and the random effect in the 1-level model.} A _ti has a value of “0, 1, 2, 3, …” as a time variable _{, and when A ti} = 0, the rate of change parameter part disappears, so _{the meaning of π 0j} becomes the meaning of the initial time parameter for each individual. have practical meaning. Therefore, when specifying the model above, time variables were coded as "0, 1, 2, 3..." and selected as [No centering]. β ₀₀ and β ₁₀ are the initial time point overall mean parameter and the overall mean rate of change parameter in the 2-level model, respectively, and are fixed effects. The dependent variable Y _ij and the intercept coefficients π _0j and π _1j above r _0j and r _1j are error terms of the 2-level model with _{π 0j} and π _{1j as dependent variables, respectively.} r _0j , r _1j are multivariate distributions with covariance.

After specifying the 1-level (time level) model in this way, the 2-level (individual level) model is specified. In the 1-level model of the multi-layered growth model, the time variable is essential, and the variables input to the other 1-level models are determined according to the researcher's research problem. If there is a variable whose characteristics change within the same individual according to the time point, and it needs to be controlled at the time level, the variable is additionally added to the 1-level model. In general, in the case of a multi-layered growth model, the model is specified by inputting only time variables at the 1-level, and the influence of individual characteristic variables on the initial time point and rate of change of the dependent variable for each individual is explored in the 2-level individual-level model. . Therefore, the research model of the multi-layered growth model adds individual characteristic variables at the 2-level.

_{First, in order to specify the first intercept coefficient (π 0j} ) of the first level, which is the initial time point parameter for each individual, the first intercept coefficient is clicked. If you click this, the regression coefficients of the two-level model are activated as shown in FIG. 8D. In addition, although not separately shown in the drawing, a centralization option is selected as in the cross-sectional model specification process. According to the variable addition/input method, the model can be specified as shown in FIG. 8E , which is an embodiment.

Next, the 3-level multilayer model will be described. The specification of the 3-level multi-layer model for the analysis of cross-sectional data uses the basic model, as in the previously described 2-level multi-layer model, and can be specified in various types of research models according to the research problem of the user. In the present invention, for convenience, it is assumed that the 3-level multi-layer data of 'student ⊂ class ⊂ school' is analyzed, and the specification of the 3-level multi-layer model will be described. <Equation 10> represents the basic model of the 3-level multi-layer model.

9 is a conceptual diagram illustrating a 3-level multi-layer model according to an embodiment of the present invention, and <Equation 11> shows the 3-level multi-layer model as shown in FIG.

β _10k is the fixed effect regression coefficient, and β _11k is the random effect regression coefficient. The two regression coefficients are regression coefficients that together explain the _{variance of π 1jk in the two-level model.} Also _{, π 2jk} , the effect of _{Z 2ijk on} the dependent variable Y _ijk , was expressed as a fixed effect in the 2-level model, but was set to have a random effect again in the 3-level model. When specifying a 3-level model in an MLM program, the intercept coefficient in each level model should have a random effect. However, for all other regression coefficients, fixed and random effects can be chosen.

The structure of the multilayer model in FIG. 9 is Y _ijk from the left, π _pjk , It is composed in the order of _{β pqk} , γ _{pqs .} Y _ijk , Up to π _pjk represents a one-level model, π _pjk , Up to β _{pqk reflects} the two-level model, and β _pqk and γ _pqs reflect the three-level model. 9, which is an embodiment, shows that π _2jk does not have an error term, but β _20k has an error term u _20k in the three-level model. That is, _{the effect of the explanatory variable Z 2ijk on} the dependent variable Y _ijk reflects the assumption that it has the same effect on all students within the same school but that there is a difference between schools.

The process of specifying the three-level model as described above on a single window screen by the apparatus for providing a multilayer model interface of the present invention using the MLM3 module will be described below with reference to FIG. 10 . In Fig. 10 according to an embodiment, it is exemplified to specify the cross-sectional model of the 3-level multi-layer model.

First, the user selects the MLM3 module through the user interface of the present invention as shown in Fig. 10a, selects the analysis type as a cross-sectional model, and then selects the 2nd level ID and 3rd level ID as shown in Figs. 10b and 10c. And, when the user selects a dependent variable through the user interface as shown in FIG. 10D, the basic model is schematically specified as shown in FIG. 10E in the apparatus for providing a multilayer model interface of the present invention.

And, when the user wants to specify the research model further from the basic model, the multilayer model interface providing apparatus of the present invention activates the _{dependent variable (Y ijk ) circle as shown in FIG. 10F according to the user's selection.} In the state shown in FIG. 10F, if you right-click the name of a variable to be input to the 1-level model in the left pane of the screen, three centering options appear. If you right-click the 'Physical Environment Satisfaction' variable, a screen as shown in FIG. 10G appears.

Referring to FIG. 10G , in the apparatus for providing a multi-layer model interface of the present invention, when a centering method desired by a user among three options is selected through the user interface, the variables are shown in the 1-level model accordingly. Here, [No Centering] means no centering, [Group mean centering] means centering the group mean, and [Grand mean centering] means centering the overall mean. When the 'physical environment satisfaction' and 'teacher position' variables are input in this way, the model is specified as shown in FIG. 10H.

As shown in Fig. 10H, which is an embodiment, when variables are added in the 1-level model, circles (r _0jk , r _1jk , r _2jk ) of the radio effect error term of the upper level are shown. If the user completes the 1-level model specification and wants to add a variable to the 2-level model, the intercept coefficient (π) treated as the dependent variable (regression coefficient) of the 2-level model in the right pane of the window screen as shown in Fig. 10h _0jk ). If this is selected, the intercept coefficient is activated as shown in FIG. 10i, and three centering options are presented by right-clicking the name of a variable to be added to the 2-level model. The centralization option has the same meaning and function as the option in the 1-level model. For example, if [No Centering] is selected among the centering options and right-clicks on the first intercept coefficient of the second level treated as the dependent variable of the 3-level model, two centering options are presented as shown in FIG. 10J. In this state, if [No Centering] is selected among the centering options, a multi-layered model as shown in FIG. 10K is specified.

Next, the cross-classification multi-layer model will be described. When the user selects a CMLM module among the MLM programs through the user interface, the device for providing a multi-layer model interface of the present invention provides diagrams according to the 2-level row group ID variable, the 2-level column group ID variable, and the dependent variable selected by the user. Specify the basic model of the cross-class multi-layered model as in 11a. In FIG. 11A, the 2-level row group ID is 'nei_id', the 2-level column group ID is 'sch_id', and the dependent variable is 'Y'. 11A is a conceptual diagram of <Equation 12> below.

where Y _ijk is the dependent variable (Y), β _0jk is the first-level intercept coefficient of the first level that is the _{random effect intercept of the 2-level model, and γ 00} is the second level of the second level that is the fixed effect intercept coefficient of the 2-level model. The first intercept coefficient, e _{ijk ,} is the error term of the 1-level model. And, the small circles a _0j , b _0k , and c _0jk on the dependent variable (Y _ijk ) and the first intercept coefficient (β _0jk ) of the first level represent error terms at each level. e _ijk is a 1-level error term, a β _0j is the error term of the line group in the 2-level model for the dependent variable _0jk, b _0k is the error term of the thermal group at the 2-level model of the β _0jk as the dependent variable, Finally, c _0jk is the error term of the cell group where the row group and the column group intersect in the 2-level model with _{β 0jk as the dependent variable.}

When the data the user wants to analyze is based on the basic model, statistical analysis can be performed later based on the model as shown in Fig. 11a, and when specifying the data as a research model, the dependent variable (Y _ijk ) is selected as shown in Fig. 11b to activate it. In the state shown in FIG. 11B, if you right-click the name of the variable (Z1) to be added to the 1-level model in the left pane of the screen, three centering options appear. The three options are [No Centering] without centering, [Group mean Centering] with group mean centering, and [Grand mean Centering], which is overall mean centering.

When 'Z1', which is the first explanatory variable of the first level, and 'Z2', which is the second explanatory variable of the first level, are selected in this way, a model as shown in FIG. 11C is specified. When variables are selected in the 1-level model as shown in FIG. 11C , the upper-level radio effect error terms a _1j , b _1k , c _1jk , a _2j , b _2k , and c _2jk are presented. In the CMLM module, when a 1-level variable is input, it is set as the default to have a radio effect at the upper level of the corresponding regression coefficient, and the radio effect can be canceled according to the model set by the user.

If you have completed the 1-level model specification and want to add variables to the 2-level model, click to activate the first intercept coefficient of the first level of the 2-level model in the right pane of the screen, Coefficients are treated as dependent variables (regression coefficients, row group variables). If you right-click the name of a variable to be added to the 2-level model in the left pane of the screen, three group membership options are presented. For the 2-level independent variable, row group characteristics, column group characteristics, and cell group characteristics are displayed. It consists of variables representing

With the first intercept coefficient of the first level treated as a regression coefficient activated, click the name of the variable you want to input into the two-level model in the left pane of the screen, and select group membership to select two centering options ([ No Centering], [Grand mean Centering]) appears. [No Centering] is no centering, and [Grand mean Centering] is the overall mean centering.

For example, if [No Centering] is selected, the multilayer model interface providing apparatus of the present invention specifies a model as shown in FIG. 11D. In the case of adding the column group variable (W1) and the cell group variable (V1) to the 2-level model, the same process as for adding the row group variable (X1) is followed. Accordingly, the multi-layer model interface providing apparatus of the present invention can specify the multi-layer model as shown in FIG. 11E. The conceptual diagram of the model according to FIG. 11E corresponds to the statistical model of <Equation 13> below.

Even if all the components constituting the embodiment of the present invention described above are described as being combined or operated in combination, the present invention is not necessarily limited to this embodiment. That is, within the scope of the object of the present invention, all the components may operate by selectively combining one or more. In addition, although all the components may be implemented as one independent hardware, some or all of the components are selectively combined to perform some or all of the functions of one or more hardware components It may be implemented as a computer program having In addition, such a computer program is stored in a computer readable media such as a USB memory, a CD disk, a flash memory, etc., read and executed by a computer, thereby implementing the embodiment of the present invention. The recording medium of the computer program may include a magnetic recording medium, an optical recording medium, and the like.

The above description is merely illustrative of the technical idea of the present invention, and various modifications, changes, and substitutions are possible within the range that does not depart from the essential characteristics of the present invention by those of ordinary skill in the art to which the present invention pertains. will be. Accordingly, the embodiments disclosed in the present invention and the accompanying drawings are for explaining, not limiting, the technical spirit of the present invention, and the scope of the technical spirit of the present invention is not limited by these embodiments and the accompanying drawings. . The protection scope of the present invention should be construed by the claims below, and all technical ideas within the scope equivalent thereto should be construed as being included in the scope of the present invention.

Claims (12)

A method for providing a multi-layer model interface performed in an information processing device, the method comprising:
The information processing apparatus includes an input unit that receives information input from a user, a processor that generates a signal to display a multi-layered model on the screen based on the inputted information, and receives the signal and provides the multi-layered model as the screen including a display unit that
displaying a 2-level multi-layer model option, a 3-level multi-layer model option, and a cross-classification multi-layer model option as a type of the multi-layer model through the display unit;
receiving the 2-level multi-layer model option, the 3-level multi-layer model option, or the cross-classification multi-layer model option through the input unit
displaying a longitudinal model option and a cross-sectional model option for the multi-layer model selected from among the types of the multi-layer model through the display unit;
receiving the longitudinal model option or the cross-sectional model option through the input unit;
receiving analysis data to be analyzed through the input unit;
receiving a dependent variable for regression analysis based on the analysis data;
displaying, by the processor, a visualized tree model including an intercept coefficient of a first level for explaining the dependent variable and an error term for the dependent variable through the display unit;
receiving a first explanatory variable of a first level describing the dependent variable through the input unit, and displaying, by the processor, adding the first explanatory variable of the first level to the visualized tree model;
Displaying a grand mean centering option, a group mean centering option, and a no centering option as a centering option for the first explanatory variable of the first level through the display unit ;
receiving one of the overall mean centering option, the group mean centering option, and the no centering option through the input unit;
Activate the intercept coefficient of the first level as a first dependent variable of a second level through the display unit, the first intercept coefficient of the second level, and the second level to describe the first dependent variable of the second level adding and displaying a first error term of a first level for an intercept coefficient of a level of one level to the visualized tree model; and
Through the display, i) activate a regression coefficient of a first explanatory variable of the first level as a second dependent variable of the second level, and ii) describe the second dependent variable of the second level A method for providing a multilayer model interface, comprising the steps of adding and displaying a second intercept coefficient of a level, and iii) a second error term of a second level for a second dependent variable of the second level in the visualized tree model. delete delete According to claim 1,
An input for canceling the setting of the second error term with respect to the second dependent variable of the second level is received through the input unit, and displayed on the display unit according to the setting cancellation of the inputted second error term of the first level by the processor The method for providing a multi-layer model interface, characterized in that it further comprises the step of deleting the variable according to the second error term of the first level. According to claim 1,
receiving, by the input unit, an input related to adding a first variable for describing the intercept coefficient of the first level;
activating, by the processor, the intercept coefficient of the first level as a first dependent variable of the second level; and
receiving the first explanatory variable of the second level for describing the first dependent variable of the second level through the input unit, and the processor is configured to cause the first level of the first explanatory variable of the second level with respect to the first dependent variable of the second level The method of providing a multi-layer model interface further comprising; adding and displaying the regression coefficients of the explanatory variables to the visualized tree model. 6. The method of claim 5,
receiving, by the input unit, an input related to adding a second variable for describing the intercept coefficient of the first level;
activating, by the processor, the intercept coefficient of the first level as a first dependent variable of the second level; and
wherein the input unit receives a second explanatory variable of a second level to describe the first dependent variable of the second level, and wherein the processor is configured to describe the first dependent variable of the second level. The method for providing a multi-layer model interface further comprising: adding and displaying a second regression coefficient of the explanatory variable to the visualized tree model. According to claim 1,
activating, by the processor, a first regression coefficient of the first level as a second dependent variable of the second level;
receiving, by the input unit, an input related to adding a variable for describing a second dependent variable of the second level; and
The input unit receives a third explanatory variable of a second level using the first regression coefficient of the first level as a dependent variable to explain the first regression coefficient of the first level, and the processor is configured to: The multi-layered model further comprising: adding and displaying a third regression coefficient of the second level with respect to the third explanatory variable of the second level to the visualized tree model to explain the third explanatory variable; How to provide an interface. According to claim 1,
The method for providing a multi-layer model interface, characterized in that the variables are listed in one area so that a plurality of variables included in the analysis data among the entire area of the screen can be visualized together with the tree model through the display unit. delete delete delete A computer program stored in a computer-readable recording medium for executing the method for providing a multi-layer model interface according to any one of claims 1 to 8 to a computer.

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