Description Usage Arguments Value Note Author(s) References Examples

Seven different plot types that visualize *p*-value influencers.

1. `lmPlot`

: plots the linear regression, marks the influencer(s) in red and displays trend lines for the full and leave-one-out (LOO) data set (black and red, respectively).

2. `pvalPlot`

: plots the *p*-values for each LOO data point and displays the values as a full model/LOO model plot, together with the `alpha`

border as defined in `lmInfl`

.

3. `inflPlot`

: plots `dfbeta`

for slope, `dffits`

, `covratio`

, `cooks.distance`

, leverage (`hatvalues`

) and studentized residuals (`rstudent`

) against the *Δ**p*-value. Herewith, changes in these six parameters can be compared to the effect on the corresponding drop/rise in *p*-value. The plots include vertical boundaries for threshold values as defined in the literature under 'References'.

4. `slsePlot`

: plots all LOO-slopes and their standard errors together with the corresponding original model values and a t-value border as calculated by *\mathit{Q_t}(1 - \frac{α}{2}, n-2)*. LOO of points on the right of this border result in a significant model, and *vice versa*.

5. `threshPlot`

: plots the output of `lmThresh`

, i.e. the regression plot including confidence/prediction intervals, as well as for each response value *y_i* the region in which the model is significant (green). This is tested for either i) *y_i* that are shifted into this region (`newobs = FALSE`

in `lmThresh`

) or ii) when a new observation *y2_i* is added (`newobs = TRUE`

in `lmThresh`

). In the latter case, it is informative if this region resides within the prediction interval (dashed line), indicating that a future additional measurement at *x_i* might reverse the significance statement.

6. `multPlot`

: plots the output of `lmMult`

as a point cloud of *p*-values for each 1...`max`

sample removals and `n`

combinations. All combinations for which the sample removal resulted in a significance reversal are colored in red, the percentages of these are given on top of the plot.

7. `stabPlot`

: for single (to be selected) response values from the output of `lmThresh`

, this function displays the region of significance reversal within the surrounding prediction interval. The probability of a either shifting the response value (if `lmThresh(..., newobs = FALSE)`

) or of including a future (measurement) point (if `lmThresh(..., newobs = TRUE)`

) to reverse the significance is shown as the integral between the "end of significance region" (eosr) and the nearest prediction interval boundary.

**NOTE**: The visual display should always be supplemented with the corresponding `stability`

analysis.

1 2 3 4 5 6 7 |

`infl` |
an object obtained from |

`thresh` |
an object obtained from |

`stab` |
an object obtained from using |

`bands` |
logical. If |

`mult` |
an object obtained from |

`log` |
should the |

`which` |
which response value should be shown in |

`...` |
other plotting parameters. |

The corresponding plot.

Cut-off values for the different influence measures are the following:

**dfbeta slope**: *| Δβ1_i | > 2/√{n}*

**dffits**: *| \mathrm{dffits}_i | > 2√{2/n}*

**covratio**: *|\mathrm{covr}_i - 1| > 3k/n*

**Cook's D**: *D_i > F(0.5, k, n - k)*; 4/(n - k)

**leverage**: *h_{ii} > 2k/n*

**studentized residual**: *t_i > t(0.975, n - k - 1)*

Andrej-Nikolai Spiess

Linear Regression Diagnostics.

Welsch RE & Kuh E.

Nber Computer Research Center (2017).

Applied Regression Analysis: A Research Tool.

Rawlings JO, Pantula SG, Dickey DA.

Springer; 2nd Corrected ed. 1998. Corr. 2nd printing 2001.

Applied Regression Analysis and Generalized Linear Models. Fox J. SAGE Publishing, 3rd ed, 2016.

1 | ```
## See Examples in 'lmInfl', 'lmThresh' and 'lmMult'.
``` |

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