Description Usage Arguments Value Author(s) See Also Examples

Five functions: `cov.2cells`

, `cov.cell.col`

, `covNijCk`

, `cov2cols`

and `covCiCj`

These are auxiliary functions for computing covariances between entries in the TCT for the types I-IV
cell-specific tests. The covariances between *T_{ij}* values for *i,j=1,…,k* in the TCT require covariances
between two cells in the NNCT, between a cell and column sum, and between two column sums in the NNCT.
`cov.2cells`

computes the covariance between two cell counts *N_{ij}* and *N_{kl}* in an NNCT,
`cov.cell.col`

and `covNijCk`

are equivalent and they compute the covariance between cell count *N_{ij}*
and sum of column *k*, *C_k*,
`cov2cols`

and `covCiCj`

are equivalent and they compute the covariance between sums of two columns,
*C_i* and *C_j*.
The index arguments refer to which entry or column sum is intended in the NNCT.
The argument `covN`

must be the covariance between *N_{ij}* values which are obtained from NNCT by row-wise vectorization.
These covariances are valid under RL or conditional on *Q* and *R* under CSR.

1 2 3 4 5 6 7 8 9 | ```
cov.2cells(i, j, k, l, ct, covN)
cov.cell.col(i, j, k, ct, covN)
covNijCk(i, j, k, ct, covN)
cov.2cols(i, j, ct, covN)
covCiCj(i, j, ct, covN)
``` |

`i, j, k, l` |
Indices of the cell counts or column sums whose covariance is to be computed. All four are
needed for |

`ct` |
A nearest neighbor contingency table |

`covN` |
The |

`cov.2cells`

returns the covariance between two cell counts *N_{ij}* and *N_{kl}* in an NNCT,
`cov.cell.col`

and `covNijCk`

return the covariance between cell count *N_{ij}*
and sum of column *k*, *C_k*,
`cov2cols`

and `covCiCj`

return the covariance between sums of two columns,
*C_i* and *C_j*.

Elvan Ceyhan

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 | ```
n<-20 #or try sample(1:20,1)
Y<-matrix(runif(3*n),ncol=3)
ipd<-ipd.mat(Y)
cls<-sample(1:2,n,replace = TRUE) #or try cls<-rep(1:2,c(10,10))
ct<-nnct(ipd,cls)
W<-Wmat(ipd)
Qv<-Qvec(W)$q
Rv<-Rval(W)
varN<-var.nnct(ct,Qv,Rv)
covN<-cov.nnct(ct,varN,Qv,Rv)
cov.2cells(1,1,1,2,ct,covN)
cov.cell.col(2,2,1,ct,covN)
covNijCk(2,2,1,ct,covN)
cov.2cols(2,1,ct,covN)
covCiCj(2,1,ct,covN)
#############
n<-40
Y<-matrix(runif(3*n),ncol=3)
ipd<-ipd.mat(Y)
cls<-sample(1:4,n,replace = TRUE) #or try cls<-rep(1:2,c(10,10))
ct<-nnct(ipd,cls)
W<-Wmat(ipd)
Qv<-Qvec(W)$q
Rv<-Rval(W)
varN<-var.nnct(ct,Qv,Rv)
covN<-cov.nnct(ct,varN,Qv,Rv)
cov.2cells(2,3,1,2,ct,covN)
cov.cell.col(1,1,2,ct,covN)
covNijCk(1,1,2,ct,covN)
cov.2cols(3,4,ct,covN)
covCiCj(3,4,ct,covN)
``` |

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