Package 'SpaCOAP'

Select the parameters in COAP models

Description

Select the number of factors and the rank of coefficient matrix in the covariate-augmented overdispersed Poisson factor model

Usage

chooseParams(
  X_count,
  Adj_sp,
  H,
  Z = matrix(1, nrow(X_count), 1),
  offset = rep(0, nrow(X_count)),
  q_max = 15,
  r_max = 24,
  threshold = c(0.1, 0.01),
  verbose = TRUE,
  ...
)

Arguments

X_count	a count matrix, the observed count matrix with shape n-by-p.
Adj_sp	a sparse matrix, the weighted adjacency matrix;
H	a n-by-d matrix, the covariate matrix with low-rank regression coefficient matrix;
Z	an optional matrix, the fixed-dimensional covariate matrix with control variables; default as a full-one column vector if there is no additional covariates.
offset	an optional vector, the offset for each unit; default as full-zero vector.
q_max	an optional string, specify the upper bound for the number of factors; default as 15.
r_max	an optional integer, specify the upper bound for the rank of the regression coefficient matrix; default as 24.
threshold	an optional 2-dimensional positive vector, specify the the thresholds that filters the singular values of beta and B, respectively.
verbose	a logical value, whether output the information in iteration.
...	other arguments passed to the function SpaCOAP.

Details

The threshold is to filter the singular values with low signal, to assist the identification of underlying model structure.

Value

return a named vector with names 'hr' and 'hq', the estimated rank and number of factors.

References

None

See Also

SpaCOAP

Examples

width <- 20; height <- 15; p <- 300
d <- 20; k <- 3; q <- 6; r <- 3
datlist <- gendata_spacoap(width=width, height=height, p=p, d=d, k=k, q=q, rank0=r)
set.seed(1)
para_vec <- chooseParams(X_count=datlist$X, Adj_sp=datlist$Adj_sp,
 H= datlist$H, Z = datlist$Z, r_max=6)
print(para_vec)

---

Generate simulated data

Description

Generate simulated data from spaital covariate-augmented Poisson factor models

Usage

gendata_spacoap(
  seed = 1,
  width = 20,
  height = 30,
  p = 500,
  d = 40,
  k = 3,
  q = 5,
  rank0 = 3,
  eta0 = 0.5,
  bandwidth = 1,
  rho = c(10, 1),
  sigma2_eps = 1,
  seed.beta = 1
)

Arguments

seed	a postive integer, the random seed for reproducibility of data generation process.
width	a postive integer, specify the width of the spatial grid.
height	a postive integer, specify the height of the spatial grid.
p	a postive integer, specify the dimension of count variables.
d	a postive integer, specify the dimension of covariate matrix with low-rank regression coefficient matrix.
k	a postive integer, specify the dimension of covariate matrix as control variables.
q	a postive integer, specify the number of factors.
rank0	a postive integer, specify the rank of the coefficient matrix.
eta0	a real between 0 and 1, specify the spatial autocorrelation parameter.
bandwidth	a real positive value, specify the bandwidth in calculating the weighted adjacency matrix.
rho	a numeric vector with length 2 and positive elements, specify the signal strength of loading matrix and regression coefficient, respectively.
sigma2_eps	a positive real, the variance of overdispersion error.
seed.beta	a postive integer, the random seed for reproducibility of data generation process by fixing the regression coefficient matrix beta.

Details

None

Value

return a list including the following components:

• X - the high-dimensional count matrix;

• Z - the low-dimensional covariate matrix with control variables.

• H - the high-dimensional covariate matrix;

• Adj_sp - the weighted adjacence matrix;

• alpha0 - the regression coefficient matrix corresponing to Z;

• bbeta0 - the low-rank large regression coefficient matrix corresponing to H;

• B0 - the loading matrix;

• F0 - the laten factor matrix;

• rank0 - the true rank of bbeta0;

• q - the true number of factors;

• eta0 - spatial autocorrelation parameter;

• pos - spatial coordinates for each observation.

References

None

See Also

SpaCOAP

Examples

width <- 20; height <- 15; p <- 100
d <- 20; k <- 3; q <- 6; r <- 3
datlist <- gendata_spacoap(width=width, height=height, p=p, d=20, k=k, q=q, rank0=r)
str(datlist)

---

Fit the SpaCOAP model

Description

Fit the spatial covariate-augmented overdispersed Poisson factor model

Usage

SpaCOAP(
  X_count,
  Adj_sp,
  H,
  Z = matrix(1, nrow(X_count), 1),
  offset = rep(0, nrow(X_count)),
  rank_use = 5,
  q = 15,
  epsELBO = 1e-08,
  maxIter = 30,
  verbose = TRUE,
  add_IC_inter = FALSE,
  seed = 1,
  algo = 1
)

Arguments

X_count	a count matrix, the observed count matrix with shape n-by-p.
Adj_sp	a sparse matrix, the weighted adjacency matrix;
H	a n-by-d matrix, the covariate matrix with low-rank regression coefficient matrix;
Z	an optional matrix, the fixed-dimensional covariate matrix with control variables; default as a full-one column vector if there is no additional covariates.
offset	an optional vector, the offset for each unit; default as full-zero vector.
rank_use	an optional integer, specify the rank of the regression coefficient matrix; default as 5.
q	an optional string, specify the number of factors; default as 15.
epsELBO	an optional positive vlaue, tolerance of relative variation rate of the envidence lower bound value, defualt as '1e-8'.
maxIter	the maximum iteration of the VEM algorithm. The default is 30.
verbose	a logical value, whether output the information in iteration.
add_IC_inter	a logical value, add the identifiability condition in iterative algorithm or add it after algorithm converges; default as FALSE.
seed	an integer, set the random seed in initialization, default as 1;
algo	an optional integer taking value 1 0r 2, select the algorithm used, default as 1, representing variational EM algorithm.

Details

None

Value

return a list including the following components:

• F - the predicted factor matrix;

• B - the estimated loading matrix;

• bbeta - the estimated low-rank large coefficient matrix;

• alpha0 - the estimated regression coefficient matrix corresponing to Z;

• invLambda - the inverse of the estimated variances of error;

• eta - the estimated spatial autocorrelation parameter;

• S - the approximated posterior covariance for each row of F;

• ELBO - the ELBO value when algorithm stops;

• ELBO_seq - the sequence of ELBO values.

• time_use - the running time in model fitting of SpaCOAP;

References

Liu W, Zhong Q. High-dimensional covariate-augmented overdispersed poisson factor model. Biometrics. 2024 Jun;80(2):ujae031.

See Also

None

Examples

width <- 20; height <- 15; p <- 100
d <- 20; k <- 3; q <- 6; r <- 3
datlist <- gendata_spacoap(width=width, height=height, p=p, d=20, k=k, q=q, rank0=r)
fitlist <- SpaCOAP(X_count=datlist$X, Adj_sp = datlist$Adj_sp, 
H= datlist$H, Z = datlist$Z, q=6, rank_use=3)
str(fitlist)

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