Examples of "intraclass"
The earliest work on intraclass correlations focused on the case of paired measurements, and the first intraclass correlation (ICC) statistics to be proposed were modifications of the interclass correlation (Pearson correlation).
"D" is also related to intraclass correlation ( ρ ) which is defined as
The left term is non-negative, consequently the intraclass correlation must satisfy
Experiments can be run with a similar setup to the one given in Table 1. Using different relationship groups, we can evaluate different intraclass correlations. Using formula_27 as the additive genetic variance and formula_28 as the dominance deviation variance, intraclass correlations become linear functions of these parameters. In general,
The formula_20 term is the intraclass correlation among half sibs. We can easily calculate formula_21. The Expected Mean Square is calculated from the relationship of the individuals (progeny within a sire are all half-sibs, for example), and an understanding of intraclass correlations.
Consider a data set consisting of "N" paired data values ("x", "x"), for "n" = 1, ..., "N". The intraclass correlation "r" originally proposed by Ronald Fisher is
The intraclass correlation is also defined for data sets with groups having more than 2 values. For groups consisting of 3 values, it is defined as
These cases always represent situations where interclass electronic excitations happen. Other three excitation schemes involve a single interclass excitation plus an intraclass excitation internal to the active space:
In statistics, the intraclass correlation (or the "intraclass correlation coefficient", abbreviated ICC) is an inferential statistic that can be used when quantitative measurements are made on units that are organized into groups. It describes how strongly units in the same group resemble each other. While it is viewed as a type of correlation, unlike most other correlation measures it operates on data structured as groups, rather than data structured as paired observations.
which can be interpreted as the fraction of the total variance that is due to variation between groups. Ronald Fisher devotes an entire chapter to Intraclass correlation in his classic book "Statistical Methods for Research Workers".
"Cancelable biometrics refers to the intentional and systematically repeatable distortion of biometric features in order to protect sensitive user-specific data. If a cancelable feature is compromised, the distortion characteristics are changed, and the same biometrics is mapped to a new template, which is used subsequently. Cancelable biometrics is one of the major categories for biometric template protection purpose besides biometric cryptosystem." In biometric cryptosystem, "the error-correcting coding techniques are employed to handle intraclass variations." This ensures a high level of security but has limitations such as specific input format of only small intraclass variations.
The key difference between this ICC and the interclass (Pearson) correlation is that the data are pooled to estimate the mean and variance. The reason for this is that in the setting where an intraclass correlation is desired, the pairs are considered to be unordered. For example, if we are studying the resemblance of twins, there is usually no meaningful way to order the values for the two individuals within a twin pair. Like the interclass correlation, the intraclass correlation for paired data will be confined to the interval [-1, +1].
One of Fleiss's chief concerns was mental health statistics, particularly assessing the reliability of diagnostic classifications, and the measures, models, and control of errors in categorization. He was among the first to notice the equivalence of weighted kappa and the intraclass correlation coefficient as measures of reliability in categorical data (see Fleiss' kappa).
Beginning with Ronald Fisher, the intraclass correlation has been regarded within the framework of analysis of variance (ANOVA), and more recently in the framework of random effects models. A number of ICC estimators have been proposed. Most of the estimators can be defined in terms of the random effects model
Since the "intraclass correlation coefficient" gives a composite of intra-observer and inter-observer variability, its results are sometimes considered difficult to interpret when the observers are not exchangeable. Alternative measures such as Cohen's kappa statistic, the Fleiss kappa, and the concordance correlation coefficient have been proposed as more suitable measures of agreement among non-exchangeable observers.
The second was originally developed by R. A. Fisher and expanded at The University of Edinburgh, Iowa State University, and North Carolina State University, as well as other schools. It is based on the analysis of variance of breeding studies, using the intraclass correlation of relatives. Various methods of estimating components of variance (and, hence, heritability) from ANOVA are used in these analyses.
The "intraclass correlation" is commonly used to quantify the degree to which individuals with a fixed degree of relatedness (e.g. full siblings) resemble each other in terms of a quantitative trait (see heritability). Another prominent application is the assessment of consistency or reproducibility of quantitative measurements made by different observers measuring the same quantity.
The second group of progeny are comparisons of means of half sibs with each other (called "among sire group"). In addition to the error term as in the within sire groups, we have an addition term due to the differences among different means of half sibs. The intraclass correlation is
A random intercepts model is a model in which intercepts are allowed to vary, and therefore, the scores on the dependent variable for each individual observation are predicted by the intercept that varies across groups. This model assumes that slopes are fixed (the same across different contexts). In addition, this model provides information about intraclass correlations, which are helpful in determining whether multilevel models are required in the first place.
The concordance correlation coefficient is nearly identical to some of the measures called intra-class correlations, and comparisons of the concordance correlation coefficient with an "ordinary" intraclass correlation on different data sets found only small differences between the two correlations, in one case on the third decimal. It has also been stated that the ideas for concordance correlation coefficient "are quite similar to results already published by Krippendorff