rxLinMod: Linear Models

2019-07-15

Description

Fit linear models on small or large data.

Usage

  rxLinMod(formula, data, pweights = NULL, fweights = NULL, cube = FALSE,
           cubePredictions = FALSE, variableSelection = list(),
           rowSelection = NULL, transforms = NULL, transformObjects = NULL,
           transformFunc = NULL, transformVars = NULL, 
           transformPackages = NULL, transformEnvir = NULL,
           dropFirst = FALSE, dropMain = rxGetOption("dropMain"),
           covCoef = FALSE, covData = FALSE, 
           coefLabelStyle = rxGetOption("coefLabelStyle"),
           blocksPerRead = rxGetOption("blocksPerRead"),
           reportProgress = rxGetOption("reportProgress"), verbose = 0,
           computeContext = rxGetOption("computeContext"),  
           ...)

Arguments

`formula`

formula as described in rxFormula.

`data`

either a data source object, a character string specifying a .xdf file, or a data frame object.

`pweights`

character string specifying the variable to use as probability weights for the observations.

`fweights`

character string specifying the variable to use as frequency weights for the observations.

`cube`

logical flag. If TRUE and the first term of the predictor variables is categorical (a factor or an interaction of factors), the regression is performed by applying the Frisch-Waugh-Lovell Theorem, which uses a partitioned inverse to save on computation time and memory. See Details section below.

`cubePredictions`

logical flag. If TRUE and cube is TRUE the predicted values are computed and included in the countDFcomponent of the returned value. This may be memory intensive. See Details section below.

`variableSelection`

a list specifying various parameters that control aspects of stepwise regression. If it is an empty list (default), no stepwise model selection will be performed. If not, stepwise regression will be performed and cube must be FALSE. See rxStepControl for details.

`rowSelection`

name of a logical variable in the data set (in quotes) or a logical expression using variables in the data set to specify row selection. For example, rowSelection = "old" will use only observations in which the value of the variable old is TRUE. rowSelection = (age > 20) & (age < 65) & (log(income) > 10) will use only observations in which the value of the age variable is between 20 and 65 and the value of the log of the income variable is greater than 10. The row selection is performed after processing any data transformations (see the arguments transforms or transformFunc). As with all expressions, rowSelection can be defined outside of the function call using the expression function.

`transforms`

an expression of the form list(name = expression, ...) representing the first round of variable transformations. As with all expressions, transforms (or rowSelection) can be defined outside of the function call using the expression function.

`transformObjects`

a named list containing objects that can be referenced by transforms, transformsFunc, and rowSelection.

`transformFunc`

variable transformation function. The variables used in the transformation function must be specified in transformVars if they are not variables used in the model. See rxTransform for details.

`transformVars`

character vector of input data set variables needed for the transformation function. See rxTransform for details.

`transformPackages`

character vector defining additional R packages (outside of those specified in rxGetOption("transformPackages")) to be made available and preloaded for use in variable transformation functions, e.g., those explicitly defined in RevoScaleR functions via their transforms and transformFunc arguments or those defined implicitly via their formula or rowSelection arguments. The transformPackages argument may also be NULL, indicating that no packages outside rxGetOption("transformPackages") will be preloaded.

`transformEnvir`

user-defined environment to serve as a parent to all environments developed internally and used for variable data transformation. If transformEnvir = NULL, a new "hash" environment with parent baseenv() is used instead.

`dropFirst`

logical flag. If FALSE, the last level is dropped in all sets of factor levels in a model. If that level has no observations (in any of the sets), or if the model as formed is otherwise determined to be singular, then an attempt is made to estimate the model by dropping the first level in all sets of factor levels. If TRUE, the starting position is to drop the first level. Note that for cube regressions, the first set of factors is excluded from these rules and the intercept is dropped.

`dropMain`

logical value. If TRUE, main-effect terms are dropped before their interactions.

`covCoef`

logical flag. If TRUE and if cube is FALSE, the variance-covariance matrix of the regression coefficients is returned. Use the rxCovCoef function to obtain these data.

`covData`

logical flag. If TRUE and if cube is FALSE and if constant term is included in the formula, then the variance-covariance matrix of the data is returned. Use the rxCovData function to obtain these data.

`coefLabelStyle`

character string specifying the coefficient label style. The default is "Revo". If "R", R-compatible labels are created.

`blocksPerRead`

number of blocks to read for each chunk of data read from the data source.

`reportProgress`

integer value with options:

0: no progress is reported.
1: the number of processed rows is printed and updated.
2: rows processed and timings are reported.
3: rows processed and all timings are reported.

`verbose`

integer value. If 0, no additional output is printed. If 1, additional summary information is printed.

`computeContext`

a valid RxComputeContext. The and RxHadoopMR compute context distributes the computation among the nodes specified by the compute context; for other compute contexts, the computation is distributed if possible on the local computer.

`...`

additional arguments to be passed directly to the Revolution Compute Engine.

Details

The special function F() can be used in formula to force a variable to be interpreted as a factor.

When cube is TRUE, the Frisch-Waugh-Lovell (FWL) Theorem is applied to the model. The FWL approach parameterizes the model to include one coefficient for each category (a single factor level or combination of factor levels) instead of using an intercept in the model with contrasts for each of the factor combinations. Additionally when cube is TRUE, the output contains a countDF element representing the counts for each category. If cubePredictions is also TRUE, predicted values using means of conditional independent continuous variables and weighted coefficients of conditional independent categorical variables are also computed and included in countDF. This may be memory intensive. If there are no conditional independent variables (outside of the cube), the predicted values are equivalent to the coefficients and will be included in countDF whenever cube is TRUE. Regardless of the setting for cube, the null model for the F-test of global significance is always the intercept-only model.

The dropFirst and dropMain arguments are provided primarily as a convenience to users comparing rxLinMod results to those of lm. While rxLinMod will sometimes drop main effects while retaining interactions involving those terms, lm will not. Setting dropMain=FALSE will give results more akin to those of lm. Similarly, lm defaults to using treatment contrasts, which essentially drop the first level of each factor from the finished model. On the other hand, rxLinMod by default uses a set of contrasts that drop the last level of each factor. Setting dropFirst=TRUE will give results more akin to those of lm.

Value

Let P be the number of regression coefficients returned for each dependent variable, Y(n) for n=1,...,N, specified in the regression model. Let X be the linear regression design matrix. The rxLinMod function returns an object of class rxLinMod, which is a list containing the following elements:

`coefficients`

P x N numeric matrix containing the regression coefficients.

`covCoef`

variance-covariance matrix for the regression coefficient estimates.

`covData`

variance-covariance matrix for the explanatory variables in the regression model.

`residual.squares`

the sum of the squares of the residuals.

`condition.number`

numeric scalar representing the estimated reciprocal condition number of X'X (moment or crossprod) matrix.

`rank`

integer scalar denoting the numeric rank of the fitted linear model.

`aliased`

logical vector specifying whether columns were dropped or not due to collinearity.

`coef.std.error`

P x N numeric matrix containing the standard errors of the regression coefficients.

`coef.t.value`

P x N numeric matrix containing the t-statistics for the regression coefficients.

`coef.p.value`

P x N numeric matrix containing the p-values for the t-stats (Pr(>|t|))

`total.squares`

N element numeric vector whose nth element is defined by Y'(n)Y(n) for n=1,...,N.

`y.var`

N element numeric vector whose nth element is defined by (Y(n) - E{Y(n)})'(Y(n) - E{Y(n)}, i.e., the mean deviation of each dependent variable.

`sigma`

N element numeric vector of standard error of residuals.

`residual.variance`

the variance of the residuals.

`r.squared`

N element numeric vector containing r-squared, the fraction of variance explained by the model.

`f.pvalue`

the p-value resulting from an F-test on the fitted model.

`df`

degrees of freedom, a 3-element vector (p, n-p, p*), the last being the number of non-aliased coefficients.

`y.names`

N element character vector containing the names of the dependent variables in the specified model.

`partitions`

when cube is TRUE, partitioned results will also be returned.

`fstatistics`

(for models including non-intercept terms) a list containing the named elements: value: an N element numeric vector of F-statistic values, numdf: corresponding numerator degrees of freedom and dendf: corresponding denominator degrees of freedom.

`adj.r.squared`

R-squared statistic 'adjusted', penalizing for higher p.

`params`

parameters sent to Microsoft R Services Compute Engine.

`formula`

the model formula. For stepwise regression, this is the final model selected.

`call`

the matched call.

`countDF`

when cube is TRUE, a data frame containing counts information for each cube. If cubePredictions is also TRUE, predicted values for each group in the cube are included.

`nValidObs`

number of valid observations.

`nMissingObs`

number of missing observations.

`deviance`

minus twice the maximized log-likelihood (up to a constant)

`anova`

for stepwise regression, a data frame corresponding to the steps taken in the search.

`formulaBase`

for stepwise regression, the base model from which the search is started.

Author(s)

Microsoft Corporation Microsoft Technical Support

References

Frisch, Ragnar; Waugh, Frederick V., Partial Time Regressions as Compared with Individual Trends, Econometrica, 1 (4) (Oct., 1933), pp. 387-401.

Lovell, M., 1963, Seasonal adjustment of economic time series, Journal of the American Statistical Association, 58, pp. 993-1010.

Lovell, M., 2008, A Simple Proof of the FWL (Frisch,Waugh,Lovell) Theorem, Journal of Economic Education.

Examples


 # Compare rxLinMod and lm, which produce similar results when contr.SAS is used
 form <- Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width + Species
 irisLinMod <- rxLinMod(form, data = iris)
 irisLinMod
 summary(irisLinMod)
 irisLM <- lm(form, data = iris, contrasts = list(Species = contr.SAS))
 summary(irisLM)

 # Instead of using the equivalent of contr.SAS, estimate the parameters
 # for the categorical levels without contrasting against an intercept term.
 # The null model for the global F-test remains the intercept-only model.
 irisCubeLinMod <-
     rxLinMod(Sepal.Length ~ Species + Sepal.Width + Petal.Length + Petal.Width,
              data = iris, cube = TRUE)
 summary(irisCubeLinMod)

 # Use the Sample Census Data
 censusWorkers <- file.path(rxGetOption("sampleDataDir"), "CensusWorkers")
 censusLinMod <- rxLinMod(wkswork1 ~ age:sex, data = censusWorkers,
                          pweights = "perwt")
 censusLinMod
 censusSubsetLinMod <- rxLinMod(wkswork1 ~ age:sex, data = censusWorkers,
                                pweights = "perwt", rowSelection = age > 39)
 censusSubsetLinMod

 # Use the Sample Airline Data and report progress during computations
 sampleDataDir <- rxGetOption("sampleDataDir")
 airlineDemoSmall <- file.path(sampleDataDir, "AirlineDemoSmall.xdf")
 airlineLinMod <- rxLinMod(ArrDelay ~ CRSDepTime, data = airlineDemoSmall,
                           reportProgress = 1)
 airlineLinMod <- rxLinMod(ArrDelay ~ CRSDepTime, data = airlineDemoSmall,
                           reportProgress = 2)
 airlineLinMod <- rxLinMod(ArrDelay ~ CRSDepTime, data = airlineDemoSmall,
                           reportProgress = 2, blocksPerRead = 3)
 summary(airlineLinMod)

 # Create a local data.frame and define a transformation  
 # function to be applied to the data prior to processing.
 myDF <- data.frame(sex = c("Male", "Male", "Female", "Male"),
                    age = c(20, 20, 12, 15), score = 1.1:4.1, sport=c(1:3,2))

 # define variable transformation list. Wrap with expression()
 # so that it is not evaluated upon assignment.
 transforms <- expression(list(
     revage = rev(age),
     division = factor(c("A","B","B","A")),
     sport = factor(sport, labels=c("tennis", "golf", "football"))))

 # Both user-defined transform and arithmetic expressions in formula.
 rxLinMod(score ~ sin(revage) + sex, data = myDF, transforms = transforms)

 # User-defined transform only.
 rxLinMod(revage ~ division + sport, data = myDF, transforms = transforms)

 # Arithmetic formula expression only.
 rxLinMod(log(score) ~ sin(age) + sex, data = myDF)

 # No variable transformations.
 rxLinMod(score ~ age + sex, data = myDF)

 # use multiple dependent variables in model formula
 # print and summarize results for comparison
 sampleDataDir <- rxGetOption("sampleDataDir")
 airlineDemoSmall <- file.path(sampleDataDir, "AirlineDemoSmall")
 airlineLinMod1 <- rxLinMod(ArrDelay ~ DayOfWeek, data = airlineDemoSmall)
 airlineLinMod2 <- rxLinMod(cbind(ArrDelay, CRSDepTime) ~ DayOfWeek,
                            data = airlineDemoSmall)
 airlineLinMod3 <-
     rxLinMod(cbind(pow(ArrDelay, 2), ArrDelay, CRSDepTime) ~ DayOfWeek,
              data = airlineDemoSmall)
 airlineLinMod4 <- rxLinMod(pow(ArrDelay, 2) ~ DayOfWeek,
                            data = airlineDemoSmall)
 airlineLinMod1
 airlineLinMod2
 airlineLinMod3
 airlineLinMod4
 summary(airlineLinMod2)

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rxLinMod: Linear Models

Description

Usage

Arguments

formula

data

pweights

fweights

cube

cubePredictions

variableSelection

rowSelection

transforms

transformObjects

transformFunc

transformVars

transformPackages

transformEnvir

dropFirst

dropMain

covCoef

covData

coefLabelStyle

blocksPerRead

reportProgress

verbose

computeContext

...

Details

Value

coefficients

covCoef

covData

residual.squares

condition.number

rank

aliased

coef.std.error

coef.t.value

coef.p.value

total.squares

y.var

sigma

residual.variance

r.squared

f.pvalue

df

y.names

partitions

fstatistics

adj.r.squared

params

formula

call

countDF

nValidObs

nMissingObs

deviance

anova

formulaBase

Author(s)

References

See Also

Examples

Feedback

Additional resources

`formula`

`data`

`pweights`

`fweights`

`cube`

`cubePredictions`

`variableSelection`

`rowSelection`

`transforms`

`transformObjects`

`transformFunc`

`transformVars`

`transformPackages`

`transformEnvir`

`dropFirst`

`dropMain`

`covCoef`

`covData`

`coefLabelStyle`

`blocksPerRead`

`reportProgress`

`verbose`

`computeContext`

`...`

`coefficients`

`covCoef`

`covData`

`residual.squares`

`condition.number`

`rank`

`aliased`

`coef.std.error`

`coef.t.value`

`coef.p.value`

`total.squares`

`y.var`

`sigma`

`residual.variance`

`r.squared`

`f.pvalue`

`df`

`y.names`

`partitions`

`fstatistics`

`adj.r.squared`

`params`

`formula`

`call`

`countDF`

`nValidObs`

`nMissingObs`

`deviance`

`anova`

`formulaBase`