Logic regression analysis using Minitab
1 logic regression overview
Logical regression and minimum square regression are to study a relationship between response variables and one or more predictors, which are logical regression techniques for category response variables, while linear regression techniques are used for continuous response variables.
Minitab provides three logical regression programs that you can use to estimate the relationship between one or more predictors and a category response variable, as shown in the following table:
Variable Category Number Characterization Sample Binary 2 Two Water Success, Failure; Yes, No Subsites 3 or More Levels Are Natural Order Relationships No, slight, severe, exquisite, medium, rough nominal 3 or more levels of non-natural sequential relationship green , Black, red, yellow; sunny, rain, cloudy
Logical regression and minimum multiplied method are performed in the model to make the model optimal, the minimum square regression is estimated to estimate the number and minimal principle, while logic regression uses iterative reloaded least squares (IRLS - ITERATIVE REWEIGHTED LEAST SQUARES) The algorithm acquires the maximum possibility to estimate the parameters.
1.1 Specified model:
Logic regression programs can construct the following model:
? More than 9 factors and more than 50 copies (COVARIATES)
? Cross and nested factors
? Co-variable amounts cross or intersect with factors, or nesting with the associator
The model's consecutive predictor is similar (Model Continuous Predictors As Covariates and Categorical Predictors as Factors), which is some examples, where A is factor, X is the coefficient.
Model item:
A x a * x Factor model with factor cross-intersector A | X An Alternative Way To Specify The Previous Model A x * x Co-variable amount with its own cross, there is a square A x (a) coast nest factor
The logical regression model is a model of more general linear regression (GLM) in Minitab, and any logic regression is built using the GLM modeling. For more general discussion model, see "Specifying The Model Terms" and "Specifying Reduced Models". In the logic regression command, Minitab assumes that any variables in any model are covariance unless it is specified as factor. In contrast, any variable of the GLM assumption model is factor unless it is designated as a covarian.
The logical regression model is a model of more general linear regression (GLM) in Minitab, any case where the GLM command modeling can also be built using the logical regression command, see "Specifying The Model". In the logic regression command, Minitab assumes that any variables in any model are covariate unless it is specified as factor, ensuring that those predictors are specified in the main dialog. In the general linear regression model, the Minitab assumes that any variables of the model are factors unless it is designated as a covarian.
Model constraint
The logical regression model in Minitab has the following constraints as the GLM model:
• There must be enough data to estimate all the models of the model, so the model is full. Minitab automatically judges whether your model is full and displays relevant information. In most cases, some unimportant high-order interactions can be solved from the model.
The model must be hierarchical, in a hierarchical model, if an interactive item is included, all the main effects of all low-order interactions and constitutive interim must appear in the model. 1.2 factor variables and reference levels
1.2.1 Factor's reference level
Minitab needs to specify a factor level as a reference level, which means that the interpretation of the estimation coefficient is related to this level. Minitab based on data type specified reference level
? Numerical factor, reference level is the minimum level
• Date / Time Factor, Reference Level is the earliest factor
• Text-type factor, reference level is the most upstanding factor in alphabetical order
You can change the default reference level in the Site dialog box.
If you have defined the order of textual factors, the default rules above are no longer applicable. Minitab Specifies the first value of your defined order as a reference level. See "Order Text Categories".
Logic returns to each factor of the model creates a set of design variables, if there is a K level, there is K-1 design variable, the reference level is encoded to 0. Below is two examples of default coding tables:
A factors have 4 levels (1 2 3 4, the reference level is 1)
A1 A2 A3 1 0 0 0 2 1 0 0 3 0 1 0 4 0 0 1
B factor has 3 levels (Temp pressure humidity, reference level is humidity)
B1 B2 Humidity 0 0 Pressure 1 0 Temp 0 1
1.2.2 Reference results for response variable
Minitab needs to specify a response value as a reference result, Minitab based on data type definition reference results:
? Numerical factor, reference results are the largest value
• Date / Time Factor, Reference result is the most recent date / time
• Text-type factor, reference results are the most backwards of alphabetical order
You can change the default reference results in the Site dialog box.
If you define the order of textual factors, the default rules are no longer applicable. Minitab Specifies the last value of your defined order as a reference result. See "Order Text Categories".
1.3 Enter the response variable data
The data sheet for entering the logical specification software can have two formats: as a source data (category) or as a collapsed. For binary logic regression, there are three other data sheet formats: As Successes and Trials, As Successes and Failures, or As Failures and Trials. Below is different formats of the same data:
As a response as Raw Data or as a Frequency Data:
Raw Data: Each observation value
C1 C2 C3 C4 Response
Factor Covariates 0
1 12 1
1 12 1
1 12.
. . 1
1 12 0
2 12 1
2 12.
. . 1
2 12.
.
Frequency Data: One line of each factor and the coastal amount
C1 C2 C3 C4 Response Count Factor Covariates 0 1 1 12 1 19 2 12 0 5 1 24 1 15 1 24 0 7 1 50 1 13.1 .1. 50 0 8 2 50 1 12 2 1 125 0 9 2 125 1 11 2 125 0 19 1 200 1 1 200 0 18 2 200 1 2 200 As a numerical input as Successes, Failures or Trials Binary response
The combination of each factor and the coastal amount is input as a row
C1
C2
C3
C4
C1
C2
C3
C4
C1
C2
C3
C4
S
T
Factor
COVAR
S
Fly
Factor
COVAR
Fly
T
Factor
COVAR
19
20
1
12
19
1
1
12
1
20
1
12
19
20
2
12
19
1
2
12
1
20
2
12
15
20
1
twenty four
15
5
1
twenty four
5
20
1
twenty four
16
20
2
twenty four
16
4
2
twenty four
4
20
2
twenty four
13
20
1
50
13
Seduce
1
50
Seduce
20
1
50
12
20
2
50
12
8
2
50
8
20
2
50
9
20
1
125
9
11
1
125
11
20
1
125
11
20
2
125
11
9
2
125
9
20
2
125
1
20
1
200
1
19
1
200
19
20
1
200
2
20
2
200
2
18
2
200
18
20
2
200
Be careful when discovering big return factories
If the absolute value of the regression coefficient is very large, it is necessary to be careful when the P-VALUE is determined. The absolute return factor is very large, and the corresponding standard deviation is also very large, making you infer of them. If you have a big absolute regression coefficient of one or more factors (coordinates), the best verification is to do logic regression including these items and logic regression does not include these items, and based on log-likelihood Changes to make inference.
If you use this way to verify the importance of the model item, your verification statistic is
-2*
Simplified Model Logo - The logarithmic similar value of the full model). test
P-Value
Method: Select
Calc> Probability Distributions> Chi-Square
. In the freedom edit box, enter the model degree of freedom of the full model - simplify the model freedom of the model, and the model freedom is the number of coefficients to be estimated. Choose
INPUT Constant
The radio box, enter the above inspection statistic, save the result in a constant, such as
K1
, Then use
Calc> Calculator
Calculate
P-Value = 1-K1
.
