constrained.estimate: Estimate parameters with constrained approach
In ZIBBSeqDiscovery: Zero-Inflated Beta-Binomial Modeling of Microbiome Count Data

Description Usage Arguments Value Author(s)

Estimate unknown parameters with constrained approach.

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constrained.estimate(m, p, q, n, betastart, bvarstart, psi.start, 
                     eta.start, gamma.start, Y, X, Y.c, ziMatrix, 
                     gn = 3)

`m`	Number of OTUs.
`p`	Number of covariates for count model (e.g., beta-binomial).
`q`	Number of covariates for zero model.
`n`	Number of samples.
`betastart`	Matrix of estimated betas, which are the effects/coefficients for the count model, with dimension p by m. It is used as initial values for the optimization procedure to estimate betas.
`bvarstart`	Matrix of variance of estimated betas with dimension p by m.
`psi.start`	Estimated vector of logit of overdispersion parameters with length m. And psi.start will be used as initial values for the optimization procedure to estimate psi.
`eta.start`	Matrix of estimated etas, which are the effects/coefficients for the zero model, with dimension q by m. It is used as initial values for the optimization procedure to estimate etas.
`gamma.start`	Estimation vector of the coefficients in the polynomial mean-overdispersion relationship in constrained approach.
`Y`	Count matrix with dimension n by m.
`X`	The design matrix (n by p, p is the number of covariates) for the count model (e.g., beta-binomial), and intercept is included.
`Y.c`	Vector of library size with length n.
`ziMatrix`	The design matrix (n by q) for the zero model, and intercept is included.
`gn`	We use a polynomial with degree of freedom gn to fit the mean-overdispersion relationship.

`betahat`	Estimation matrix of beta (p by m).
`bvar`	Estimation matrix of the variance of estimated betahat (p by m).
`psi`	Estimation vector of the logit of the overdispersion parameters (with length m).
`eta`	Estimation matrix of eta (q by m).