loddsratio | R Documentation |

Computes (log) odds ratios and their asymptotic variance covariance matrix for R x C (x strata) tables. Odds ratios are calculated for two array dimensions, separately for each level of all stratifying dimensions. See Friendly et al. (2011) for a sketch of a general theory.

loddsratio(x, ...) ## Default S3 method: loddsratio(x, strata = NULL, log = TRUE, ref = NULL, correct = any(x == 0L), ...) ## S3 method for class 'formula' loddsratio(formula, data = NULL, ..., subset = NULL, na.action = NULL) oddsratio(x, stratum = NULL, log = TRUE) ## S3 method for class 'loddsratio' coef(object, log = object$log, ...) ## S3 method for class 'loddsratio' vcov(object, log = object$log, ...) ## S3 method for class 'loddsratio' print(x, log = x$log, ...) ## S3 method for class 'loddsratio' confint(object, parm, level = 0.95, log = object$log, ...) ## S3 method for class 'loddsratio' as.array(x, log=x$log, ...) ## S3 method for class 'loddsratio' t(x) ## S3 method for class 'loddsratio' aperm(a, perm, ...)

`x` |
an object. For the default method a k-way matrix/table/array of frequencies. The number of margins has to be at least 2. |

`strata, stratum` |
Numeric or character indicating the margins of a
$k$-way table |

`ref` |
numeric or character. Reference categories for the (non-stratum) row and column dimensions that should be employed for computing the odds ratios. By default, odds ratios for profile contrasts (or sequential contrasts, i.e., successive differences of adjacent categories) are used. See details below. |

`formula` |
a formula specifying the variables used to create a
contingency table from |

`data` |
either a data frame, or an object of class |

`subset` |
an optional vector specifying a subset of observations to be used. |

`na.action` |
a function which indicates what should happen when
the data contain |

`log` |
logical. Should the results be displayed on a log scale
or not? All internal computations are always on the log-scale but the
results are transformed by default if |

`correct` |
logical or numeric. Should a continuity correction
be applied before computing odds ratios?
If |

`a, object` |
an object of class |

`perm` |
numeric or character vector specifying a permutation of strata. |

`...` |
arguments passed to methods. |

`parm` |
a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered. |

`level` |
the confidence level required for the |

For an R x C table, (log) odds ratios are formed for the set of (R-1) x (C-1)
2 x 2 tables, corresponding to some set of contrasts among the row and column
variables. The `ref`

argument allows these to be specified in a general
way.

`ref = NULL`

(default) corresponds to “profile contrasts”
(or sequential contrasts or successive differences) for ordered categories,
i.e., R1–R2, R2–R3, R3–R4, etc., and similarly for the column categories.
These are sometimes called “local odds ratios”.

`ref = 1`

gives contrasts with the first category; `ref = dim(x)`

gives contrasts with the last category; `ref = c(2, 4)`

or `ref = list(2, 4)`

corresponds to the reference being the second category in rows and
the fourth in columns.

Combinations like `ref = list(NULL, 3)`

are also possible, as are character
vectors, e.g., `ref = c("foo", "bar")`

also works ("foo" pertaining again to the
row reference and "bar" to column reference).

Note that all such parameterizations are equivalent, in that one can derive all other possible odds ratios from any non-redundant set, but the interpretation of these values depends on the parameterization.

Note also that these reference level parameterizations only have meaning when the primary (non-strata) table dimensions are larger than 2x2. In the 2x2 case, the odds ratios are defined by the order of levels of those variables in the table, so you can achieve a desired interpretation by manipulating the table.

See the help page of `plot.loddsratio`

for visualization methods.

An object of class `loddsratio`

, with the following components:

`coefficients` |
A named vector, of length (R-1) x (C-1) x |

`vcov` |
Variance covariance matrix of the log odds ratios. |

`dimnames` |
Dimension names for the log odds ratios, considered as a table of
size (R-1, C-1, |

`dim` |
Corresponding dimension vector. |

`contrasts` |
A matrix C, such that |

`log` |
A logical, indicating the value of |

The method of calculation is an example of the use of the delta method described by Agresti (2013), Section 16.1.6, giving estimates of log odds ratios and their asymptotic covariance matrix.

The `coef`

method returns the `coefficients`

component as a vector
of length (R-1) x (C-1) x `prod(dim(x)[strata])`

.
The `dim`

and `dimnames`

methods provide the proper attributes for
treating the `coefficients`

vector as an (R-1) x (C-1) x strata array.
`as.matrix`

and `as.array`

methods are also provided for this purpose.

The `confint`

method computes confidence intervals for the log odds ratios
(or for odds ratios, with `log = FALSE`

).
The `coeftest`

method (`summary`

is an alias)
prints the asymptotic standard errors, z tests (standardized log odds
ratios), and the corresponding p values.

*Structural zeros*: In addition to the options for zero cells provided by `correct`

,
the function allows for structural zeros to be represented as `NA`

in the data argument.
`NA`

in the data yields `NA`

as the `LOR`

estimate, but does not affect other
cells.

`oddsratio`

is just an alias to `loddsratio`

for backward
compatibility.

Achim Zeileis, Michael Friendly and David Meyer.

A. Agresti (2013), *Categorical Data Analysis*, 3rd Ed. New York: Wiley.

Fleiss, J. L. (1981). *Statistical Methods for Rates and Proportions*.
2nd Edition. New York: Wiley.

M. Friendly (2000), *Visualizing Categorical Data*. SAS Institute, Cary, NC.

Friendly, M., Turner, H,, Firth, D., Zeileis, A. (2011).
*Advances in Visualizing Categorical Data Using the vcd, gnm and vcdExtra Packages in R*.
Correspondence Analysis and Related Methods (CARME 2011).
http://www.datavis.ca/papers/adv-vcd-4up.pdf

`plot.loddsratio`

for some plotting methods;
`confint`

for confidence intervals;
`coeftest`

for z-tests of significance

## artificial example set.seed(1) x <- matrix(rpois(5 * 3, 7), ncol = 5, nrow = 3) dimnames(x) <- list(Row = head(letters, 3), Col = tail(letters, 5)) x_lor <- loddsratio(x) coef(x_lor) x_lor confint(x_lor) summary(x_lor) ## 2 x 2 x k cases #data(CoalMiners, package = "vcd") lor_CM <- loddsratio(CoalMiners) lor_CM coef(lor_CM) confint(lor_CM) confint(lor_CM, log = FALSE) ## 2 x k x 2 lor_Emp <-loddsratio(Employment) lor_Emp confint(lor_Emp) ## 4 way tables data(Punishment, package = "vcd") lor_pun <- loddsratio(Freq ~ memory + attitude | age + education, data = Punishment) lor_pun confint(lor_pun) summary(lor_pun) # fit linear model using WLS lor_pun_df <- as.data.frame(lor_pun) pun_mod1 <- lm(LOR ~ as.numeric(age) * as.numeric(education), data = lor_pun_df, weights = 1 / ASE^2) anova(pun_mod1) ## illustrate ref levels VA.fem <- xtabs(Freq ~ left + right, subset=gender=="female", data=VisualAcuity) VA.fem loddsratio(VA.fem) # profile contrasts loddsratio(VA.fem, ref=1) # contrasts against level 1 loddsratio(VA.fem, ref=dim(VA.fem)) # contrasts against level 4

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