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<p align="center"> Table 4</p>
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MD033 - Inline HTML

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Inline HTML
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* **Complete Dominance** - One predictor is said to completely dominate another predictor if its dominance holds across all possible subset models (that do not include the two predictors under comparison). Back to the four-predictor model, for example, complete dominance of X<sub>1</sub> over X<sub>2</sub> is achieved if the additional R<sup>2</sup> contribution of X<sub>1</sub> is more than that of X<sub>2</sub> to the null model, the model consisting of X<sub>3</sub>, the model consisting of X<sub>4</sub>, and the model consisting of both X<sub>3</sub> and X<sub>4</sub>. In Table 3, we can see that incremental R<sup>2</sup> of X<sub>1</sub> is greater than that of X<sub>2</sub> for all subset models and hence X<sub>1</sub> completely dominates X<sub>2</sub>.
Severity: Info
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MD033 - Inline HTML

Tags: html

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This rule is triggered whenever raw HTML is used in a markdown document:

Inline HTML header

To fix this, use 'pure' markdown instead of including raw HTML:

# Markdown header

Rationale: Raw HTML is allowed in markdown, but this rule is included for those who want their documents to only include "pure" markdown, or for those who are rendering markdown documents in something other than HTML.

Trailing spaces
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The library can be used in combination with Principal Component Analysis (PCA) or Factor Analysis or any other feature reduction algorithm for getting accurate and intuitive importance of predictors. The purpose of determining predictor importance in the context of Dominance Analysis is not model selection but rather uncovering the individual contributions of the predictors.
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Found in paper.md by markdownlint

MD009 - Trailing spaces

Tags: whitespace

Aliases: no-trailing-spaces

Parameters: br_spaces (number; default: 0)

This rule is triggered on any lines that end with whitespace. To fix this, find the line that is triggered and remove any trailing spaces from the end.

The brspaces parameter allows an exception to this rule for a specific amount of trailing spaces used to insert an explicit line break/br element. For example, set brspaces to 2 to allow exactly 2 spaces at the end of a line.

Note: you have to set brspaces to 2 or higher for this exception to take effect - you can't insert a br element with just a single trailing space, so if you set brspaces to 1, the exception will be disabled, just as if it was set to the default of 0.

Inline HTML
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* **Complete Dominance** - One predictor is said to completely dominate another predictor if its dominance holds across all possible subset models (that do not include the two predictors under comparison). Back to the four-predictor model, for example, complete dominance of X<sub>1</sub> over X<sub>2</sub> is achieved if the additional R<sup>2</sup> contribution of X<sub>1</sub> is more than that of X<sub>2</sub> to the null model, the model consisting of X<sub>3</sub>, the model consisting of X<sub>4</sub>, and the model consisting of both X<sub>3</sub> and X<sub>4</sub>. In Table 3, we can see that incremental R<sup>2</sup> of X<sub>1</sub> is greater than that of X<sub>2</sub> for all subset models and hence X<sub>1</sub> completely dominates X<sub>2</sub>.
Severity: Info
Found in README.md by markdownlint

MD033 - Inline HTML

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This rule is triggered whenever raw HTML is used in a markdown document:

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# Markdown header

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Line length
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\item which aspects of a service influence how likely a customer would recommend a company to others.
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MD013 - Line length

Tags: line_length

Aliases: line-length Parameters: linelength, codeblocks, tables (number; default 80, boolean; default true)

This rule is triggered when there are lines that are longer than the configured line length (default: 80 characters). To fix this, split the line up into multiple lines.

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You also have the option to exclude this rule for code blocks and tables. To do this, set the code_blocks and/or tables parameters to false.

Code blocks are included in this rule by default since it is often a requirement for document readability, and tentatively compatible with code rules. Still, some languages do not lend themselves to short lines.

Inline HTML
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* **Complete Dominance** - One predictor is said to completely dominate another predictor if its dominance holds across all possible subset models (that do not include the two predictors under comparison). Back to the four-predictor model, for example, complete dominance of X<sub>1</sub> over X<sub>2</sub> is achieved if the additional R<sup>2</sup> contribution of X<sub>1</sub> is more than that of X<sub>2</sub> to the null model, the model consisting of X<sub>3</sub>, the model consisting of X<sub>4</sub>, and the model consisting of both X<sub>3</sub> and X<sub>4</sub>. In Table 3, we can see that incremental R<sup>2</sup> of X<sub>1</sub> is greater than that of X<sub>2</sub> for all subset models and hence X<sub>1</sub> completely dominates X<sub>2</sub>.
Severity: Info
Found in README.md by markdownlint

MD033 - Inline HTML

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This rule is triggered whenever raw HTML is used in a markdown document:

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# Markdown header

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Line length
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For each predictor variable, the library  lists out all the predictors that are dominated generally, conditionally, and completely by it.
Severity: Info
Found in paper.md by markdownlint

MD013 - Line length

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Aliases: line-length Parameters: linelength, codeblocks, tables (number; default 80, boolean; default true)

This rule is triggered when there are lines that are longer than the configured line length (default: 80 characters). To fix this, split the line up into multiple lines.

This rule has an exception where there is no whitespace beyond the configured line length. This allows you to still include items such as long URLs without being forced to break them in the middle.

You also have the option to exclude this rule for code blocks and tables. To do this, set the code_blocks and/or tables parameters to false.

Code blocks are included in this rule by default since it is often a requirement for document readability, and tentatively compatible with code rules. Still, some languages do not lend themselves to short lines.

Inline HTML
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<img src='images/Breast_Cancer_Data_Dominance_Latest.JPG'>
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MD033 - Inline HTML

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This rule is triggered whenever raw HTML is used in a markdown document:

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# Markdown header

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Inline HTML
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<img src='images/pie_breast_cancer_latest.png'>
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Found in README.md by markdownlint

MD033 - Inline HTML

Tags: html

Aliases: no-inline-html

This rule is triggered whenever raw HTML is used in a markdown document:

Inline HTML header

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# Markdown header

Rationale: Raw HTML is allowed in markdown, but this rule is included for those who want their documents to only include "pure" markdown, or for those who are rendering markdown documents in something other than HTML.

Inline HTML
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<hr>
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MD033 - Inline HTML

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This rule is triggered whenever raw HTML is used in a markdown document:

Inline HTML header

To fix this, use 'pure' markdown instead of including raw HTML:

# Markdown header

Rationale: Raw HTML is allowed in markdown, but this rule is included for those who want their documents to only include "pure" markdown, or for those who are rendering markdown documents in something other than HTML.

Inline HTML
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<hr>
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Found in README.md by markdownlint

MD033 - Inline HTML

Tags: html

Aliases: no-inline-html

This rule is triggered whenever raw HTML is used in a markdown document:

Inline HTML header

To fix this, use 'pure' markdown instead of including raw HTML:

# Markdown header

Rationale: Raw HTML is allowed in markdown, but this rule is included for those who want their documents to only include "pure" markdown, or for those who are rendering markdown documents in something other than HTML.

Inline HTML
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<hr>
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Found in README.md by markdownlint

MD033 - Inline HTML

Tags: html

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This rule is triggered whenever raw HTML is used in a markdown document:

Inline HTML header

To fix this, use 'pure' markdown instead of including raw HTML:

# Markdown header

Rationale: Raw HTML is allowed in markdown, but this rule is included for those who want their documents to only include "pure" markdown, or for those who are rendering markdown documents in something other than HTML.

Inline HTML
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**Getting R<sup>2</sup> of the Complete Model**
Severity: Info
Found in README.md by markdownlint

MD033 - Inline HTML

Tags: html

Aliases: no-inline-html

This rule is triggered whenever raw HTML is used in a markdown document:

Inline HTML header

To fix this, use 'pure' markdown instead of including raw HTML:

# Markdown header

Rationale: Raw HTML is allowed in markdown, but this rule is included for those who want their documents to only include "pure" markdown, or for those who are rendering markdown documents in something other than HTML.

Inline HTML
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<img src='images/WaterFall_Boston_cov.png'>
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Found in README.md by markdownlint

MD033 - Inline HTML

Tags: html

Aliases: no-inline-html

This rule is triggered whenever raw HTML is used in a markdown document:

Inline HTML header

To fix this, use 'pure' markdown instead of including raw HTML:

# Markdown header

Rationale: Raw HTML is allowed in markdown, but this rule is included for those who want their documents to only include "pure" markdown, or for those who are rendering markdown documents in something other than HTML.

Bare URL used
Open

7. Luo, W., & Azen, R. (2013). Determining Predictor Importance in Hierarchical Linear Models Using Dominance Analysis. Journal of Educational and Behavioral Statistics, 38(1), 3-31. https://doi.org/10.3102/1076998612458319
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Found in README.md by markdownlint

MD034 - Bare URL used

Tags: links, url

Aliases: no-bare-urls

This rule is triggered whenever a URL is given that isn't surrounded by angle brackets:

For more information, see http://www.example.com/.

To fix this, add angle brackets around the URL:

For more information, see <http:></http:>.

Rationale: Without angle brackets, the URL isn't converted into a link in many markdown parsers.

Note: if you do want a bare URL without it being converted into a link, enclose it in a code block, otherwise in some markdown parsers it will be converted:

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Header style
Open

Dominance Levels
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Found in paper.md by markdownlint

MD003 - Header style

Tags: headers

Aliases: header-style

Parameters: style ("consistent", "atx", "atxclosed", "setext", "setextwith_atx"; default "consistent")

This rule is triggered when different header styles (atx, setext, and 'closed' atx) are used in the same document:

# ATX style H1

## Closed ATX style H2 ##

Setext style H1
===============

Be consistent with the style of header used in a document:

# ATX style H1

## ATX style H2

The setextwithatx doc style allows atx-style headers of level 3 or more in documents with setext style headers:

Setext style H1
===============

Setext style H2
---------------

### ATX style H3

Note: the configured header style can be a specific style to use (atx, atxclosed, setext, setextwith_atx), or simply require that the usage be consistent within the document.

Line length
Open

This package is designed to get an intuitive and accurate global explanation to Machine Learning Models by determining the relative importance of predictors in the dataset. The package supports classification and regression models. The determination of relative importance depends on how one defines importance. Budescu et.al [@budescu:1993; @Razia:2001; @Razia:2003] proposed using dominance analysis (DA) because it invokes a general and intuitive definition of "relative importance" that is based on the additional contribution of a predictor in all subset models. The purpose of determining predictor importance in the context of DA is not model selection but rather uncovering the individual contributions of the predictors.
Severity: Info
Found in paper.md by markdownlint

MD013 - Line length

Tags: line_length

Aliases: line-length Parameters: linelength, codeblocks, tables (number; default 80, boolean; default true)

This rule is triggered when there are lines that are longer than the configured line length (default: 80 characters). To fix this, split the line up into multiple lines.

This rule has an exception where there is no whitespace beyond the configured line length. This allows you to still include items such as long URLs without being forced to break them in the middle.

You also have the option to exclude this rule for code blocks and tables. To do this, set the code_blocks and/or tables parameters to false.

Code blocks are included in this rule by default since it is often a requirement for document readability, and tentatively compatible with code rules. Still, some languages do not lend themselves to short lines.

Line length
Open

Let's consider a scenario where we have 4 predictors; $X_1$, $X_2$, $X_3$ and $X_4$. We will have to build a total of $2^4$-1 models i.e. 15 models - $^4C_1$ = 4 models with only one predictor, $^4C_2$ = 6 models with two predictors each, $^4C_3$ = 4 models with three predictors each and 1 ($^4C_4$) complete model with all 4 predictors. Thus, the additional contributions of $X_1$ are computed as the increases in the proportion of variance accounted for when $X_1$ is added to each subset of the remaining predictors (i.e., the null subset $\{.\}$, $\{X_2\}$, $\{X_3\}$, $\{X_4\}$, $\{X_2X_3\}$, $\{X_2X_4\}$, $\{X_3X_4\}$ and $\{X_2X_3X_4\}$). Similarly, the additional contributions of $X_2$ are the increases in the proportion of variance accounted for when $X_2$ is added to each subset of the remaining predictors (i.e., the null subset $\{.\}$, $\{X_1\}$, $\{X_3\}$, $\{X_4\}$, $\{X_1X_3\}$, $\{X_1X_4\}$, $\{X_3X_4\}$ and $\{X_1X_3X_4\}$).
Severity: Info
Found in paper.md by markdownlint

MD013 - Line length

Tags: line_length

Aliases: line-length Parameters: linelength, codeblocks, tables (number; default 80, boolean; default true)

This rule is triggered when there are lines that are longer than the configured line length (default: 80 characters). To fix this, split the line up into multiple lines.

This rule has an exception where there is no whitespace beyond the configured line length. This allows you to still include items such as long URLs without being forced to break them in the middle.

You also have the option to exclude this rule for code blocks and tables. To do this, set the code_blocks and/or tables parameters to false.

Code blocks are included in this rule by default since it is often a requirement for document readability, and tentatively compatible with code rules. Still, some languages do not lend themselves to short lines.

Line length
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The \autoref{fig:formulas} is the illustration of formulas used to compute the averaged additional contributions of $X_1$ and $X_2$ within model size in the population with four predictors (we use the notation $\rho^2_{Y.X}$ to represent the proportion of variance in $Y$ that is accounted for by the predictors in the model $X$. For example, $\rho^2_{Y.X_1X_3}$ represents the proportion of variance in $Y$ that is accounted for by the model consisting of $X_1$ and $X_3$. The additional contribution of a given predictor is measured by the increase in the proportion of variance that results from adding that predictor to the regression model):
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Found in paper.md by markdownlint

MD013 - Line length

Tags: line_length

Aliases: line-length Parameters: linelength, codeblocks, tables (number; default 80, boolean; default true)

This rule is triggered when there are lines that are longer than the configured line length (default: 80 characters). To fix this, split the line up into multiple lines.

This rule has an exception where there is no whitespace beyond the configured line length. This allows you to still include items such as long URLs without being forced to break them in the middle.

You also have the option to exclude this rule for code blocks and tables. To do this, set the code_blocks and/or tables parameters to false.

Code blocks are included in this rule by default since it is often a requirement for document readability, and tentatively compatible with code rules. Still, some languages do not lend themselves to short lines.

Line length
Open

1. **Complete Dominance:** A predictor is said to completely dominate another predictor if its dominance holds across all possible subset models (that do not include the two predictors under comparison). For example, in a four-predictor model, $X_1$ is said to have complete dominance over $X_2$ when the additional R-square contribution of $X_1$ is more than that of $X_2$ for all subset models i.e. to the null model, the model consisting of $X_3$, the model consisting of $X_4$, and the model consisting of both $X_3$ and $X_4$.
Severity: Info
Found in paper.md by markdownlint

MD013 - Line length

Tags: line_length

Aliases: line-length Parameters: linelength, codeblocks, tables (number; default 80, boolean; default true)

This rule is triggered when there are lines that are longer than the configured line length (default: 80 characters). To fix this, split the line up into multiple lines.

This rule has an exception where there is no whitespace beyond the configured line length. This allows you to still include items such as long URLs without being forced to break them in the middle.

You also have the option to exclude this rule for code blocks and tables. To do this, set the code_blocks and/or tables parameters to false.

Code blocks are included in this rule by default since it is often a requirement for document readability, and tentatively compatible with code rules. Still, some languages do not lend themselves to short lines.

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