ordinal_cohens_kappa function

Computes the estimated ordinal Cohen's kappa of an ordinal time series

ordinal_cohens_kappa computes the estimated ordinal Cohen's kappa of an ordinal time series UTF-8

ordinal_cohens_kappa(series, states, distance = "Block", lag = 1)

Arguments

• series: An OTS.
• states: A numerical vector containing the corresponding states.
• distance: A function defining the underlying distance between states. The Hamming, block and Euclidean distances are already implemented by means of the arguments "Hamming", "Block" (default) and "Euclidean". Otherwise, a function taking as input two states must be provided.
• lag: The considered lag.

Returns

The estimated ordinal Cohen's kappa.

Details

Given an OTS of length $T$ with range $\mathcal{S}=\{s_0, s_1, s_2, \ldots, s_n\}$ ($s_0 < s_1 < s_2 < \ldots < s_n$), $\overline{X}_t=\{\overline{X}_1,\ldots, \overline{X}_T\}$, the function computes the estimated ordinal Cohen's kappa given by $\widehat{\kappa}_d(l)=\frac{\widehat{disp}_d(X_t)-\widehat{E}[d(X_t, X_{t-l})]}{{\widehat{disp}}_d(X_t)}$, where $\widehat{disp}_{d}(X_t)=\frac{T}{T-1}\sum_{i,j=0}^nd\big(s_i, s_j\big)\widehat{p}_i\widehat{p}_j$ is the DIVC estimate of the dispersion, with $d(\cdot, \cdot)$ being a distance between ordinal states and $\widehat{p}_k$ being the standard estimate of the marginal probability for state $s_k$, and $\widehat{E}[d(X_t, X_{t-l})]=\frac{1}{T-l} \sum_{t=l+1}^T d(\overline{X}_t, \overline{X}_{t-l})$.

Examples

estimated_ock <- ordinal_cohens_kappa(series = AustrianWages$data[[100]],
states = 0 : 5) # Computing the estimated ordinal Cohen's kappa
# for one series in dataset AustrianWages using the block distance

References

Rdpack::insert_ref(key="weiss2019distance",package="otsfeatures")

Author(s)

Ángel López-Oriona, José A. Vilar