# Class of Families to be used in the EBarrays package

### Description

Objects used as family in the `emfit`

function.

The package contains three functions that create such objects for the three most commonly used families, Gamma-Gamma, Lognormal-Normal and Lognormal-Normal with modified variances. Users may create their own families as well.

### Usage

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### Details

The `emfit`

function can potentially fit models
corresponding to several different Bayesian conjugate families. This
is specified as the `family`

argument, which ultimately has to be
an object of formal class “ebarraysFamily” with some specific slots
that determine the behavior of the ‘family’.

For users who are content to use the predefined GG, LNN and LNNMV models, no
further details than that given in the documentation for
`emfit`

are necessary. If you wish to create your own
families, read on.

### Value

Objects of class “ebarraysFamily” for the three predefined families Gamma-Gamma , Lognormal-Normal and Lognormal-Normal with modified variances.

### Objects from the Class

Objects of class “ebarraysFamily” can be created by calls of the
form `new("ebarraysFamily", ...)`

. Predefined objects
corresponding to the GG, LNN and LNNMV models can be created by
`eb.createFamilyGG()`

, `eb.createFamilyLNN()`

and
`eb.createFamilyLNNMV()`

. The same
effect is achieved by coercing from the strings `"GG"`

, `"LNN"`

and `"LNNMV"`

by `as("GG", "ebarraysFamily")`

, ```
as("LNN",
"ebarraysFamily")
```

and `as("LNNMV", "ebarraysFamily")`

.

### Slots

An object of class “ebarraysFamily” extends the class
`"character"`

(representing a short hand name for the class) and
should have the following slots (for more details see the source
code):

`description`

:-
A not too long character string describing the family

`link`

:-
function that maps user-visible parameters to the parametrization that would be used in the optimization step (e.g.

`log(sigma^2)`

for LNN). This allows the user to think in terms of familiar parametrization that may not necessarily be the best when optimizing w.r.t. those parameters. `invlink`

:-
inverse of the link function

`thetaInit`

:-
function of a single argument

`data`

(matrix containing raw expression values), that calculates and returns as a numeric vector initial estimates of the parameters (in the parametrization used for optimization) `f0`

:-
function taking arguments

`theta`

and a list called`args`

.`f0`

calculates the negative log likelihood at the given parameter value`theta`

(again, in the parametrization used for optimization). This is called from`emfit`

. When called, only genes with positive intensities across all samples are used. `f0.pp`

:-
`f0.pp`

is essentially the same as`f0`

except the terms common to the numerator and denominator when calculating posterior odds may be removed. It is called from`postprob`

. `f0.arglist`

:-
function that takes arguments

`data`

,`patterns`

(of class “ebarraysPatterns”) and`groupid`

(for LNNMV family only) and returns a list with two components,`common.args`

and`pattern.args`

.`common.args`

is a list of arguments to`f0`

that don't change from one pattern to another, whereas`pattern.args[[i]][[j]]`

is a similar list of arguments, but specific to the columns in`pattern[[i]][[j]]`

. Eventually, the two components will be combined for each pattern and used as the`args`

argument to`f0`

. `logDensity`

:-
function of two arguments

`x`

(data vector, containing log expressions) and`theta`

(parameters in user-visible parametrization). Returns log marginal density of the natural log of intensity for the corresponding theoretical model. Used in`plotMarginal`

`lower.bound`

:-
vector of lower bounds for the argument

`theta`

of`f0`

. Used in`optim`

`upper.bound`

:-
vector of upper bounds for the argument

`theta`

of`f0`

.

### Author(s)

Ming Yuan, Ping Wang, Deepayan Sarkar, Michael Newton, and Christina Kendziorski

### References

Newton, M.A., Kendziorski, C.M., Richmond, C.S., Blattner, F.R. (2001). On differential variability of expression ratios: Improving statistical inference about gene expression changes from microarray data. Journal of Computational Biology 8:37-52.

Kendziorski, C.M., Newton, M.A., Lan, H., Gould, M.N. (2003). On parametric empirical Bayes methods for comparing multiple groups using replicated gene expression profiles. Statistics in Medicine 22:3899-3914.

Newton, M.A. and Kendziorski, C.M. Parametric Empirical Bayes Methods for Microarrays in The analysis of gene expression data: methods and software. Eds. G. Parmigiani, E.S. Garrett, R. Irizarry and S.L. Zeger, New York: Springer Verlag, 2003.

Newton, M.A., Noueiry, A., Sarkar, D., and Ahlquist, P. (2004). Detecting differential gene expression with a semiparametric hierarchical mixture model. Biostatistics 5: 155-176.

Yuan, M. and Kendziorski, C. (2006). A unified approach for simultaneous gene clustering and differential expression identification. Biometrics 62(4): 1089-1098.

### See Also

`emfit`

, `optim`

, `plotMarginal`

### Examples

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