HGGRAPH procedure

Draws a graph to display the fit of an HGLM or DHGLM analysis (R.W. Payne, Y. Lee, J.A. Nelder & M. Noh).

Options

GRAPHICS = string token	Type of graphics to use (lineprinter, highresolution); default high
TITLE = text	Title for the graph; default * sets an appropriate title automatically
WINDOW = number	Which high-resolution graphics window to use; default 4 (redefined if necessary to fill the frame)
SCREEN = string token	Whether to clear the graphics screen before plotting (clear, keep); default clea
BACKTRANSFORM = string token	What back-transformation to make (link, none, axis); default none
OMITRESPONSE = string token	Whether to omit the adjusted response values (no, yes); default no
SAVE = pointer	Specifies the save structure (from HGANALYSE) of the analysis from which to predict; default uses the most recent analysis

Parameters

INDEX = variates or factors	Which variate or factor to display along the x-axis; default * if GROUPS is set, otherwise INDEX is set to the first variate in the fixed model
GROUPS = factors	Factor to define groups of points to display; default * if INDEX is set, otherwise GROUPS is set to the first factor in the fixed model

Description

HGGRAPH is one of several procedures with the prefix HG, which provide tools for fitting the hierarchical and double hierarchical generalized linear models (HGLMs and DHGLMs) defined by Lee & Nelder (1996, 2001, 2006) and described by Lee, Nelder & Pawitan (2006). The models are defined by the HGFIXEDMODEL, HGRANDOMMODEL and HGDRANDOMMODEL procedures, and fitted by the HGANALYSE procedure. HGGRAPH has a similar role to the RGRAPH procedure in ordinary regression and generalized linear models. It displays the fitted model in one or two dimensions. It usually also displays the observed response values, adjusted for any other explanatory terms in the model, but these can be omitted by setting option OMITRESPONSE=yes.

The dimensions to display are specified by the INDEX and GROUPS parameters. The INDEX vector, which can be either a variate or a factor from the fixed model of the HGLM, defines the x-axis of the plot. (The y-axis corresponds to the response scale.) The GROUPS parameter can be set to another factor from the fixed model. A set of points is then plotted for each level of GROUPS, so that you can study the interaction between GROUPS and INDEX. If INDEX and GROUPS are not set, HGGRAPH takes the first variate (if any) and the first factor in the fixed model.

The relationship is usually plotted on the scale of the linear predictor. However, with a conjugate HGLM, you can set option BACKTRANSFORM=link to use the original scale of the response. Alternatively, you can set BACKTRANSFORM=axis to include axis markings, back-transformed onto the natural scale, on the right-hand side of the y-axis. However, this is not available for the reciprocal link.

The TITLE option can be used to supply a title for the graph. By default the graph is plotted on the current high-resolution device, but the GRAPHICS option can be set to line for a line printer plot. The WINDOW option can be used to select a pre-defined window for high-resolution plots; otherwise window 4 is used, and is redefined if necessary to fill the frame. The SCREEN option allows the graph to be added to an existing high-resolution plot. The colours and symbols used in the displays can be controlled by setting the attributes of the following pens with the PEN directive before calling the procedure:

pen 1	labels for lines when drawn for each level of a factor,
pen 2	fitted lines and means,
pen 3	points, and
pen 4	back-transformed axis marks and labels.

Options: GRAPHICS, TITLE, WINDOW, SCREEN, BACKTRANSFORM, OMITRESPONSE, SAVE.

Parameters: INDEX, GROUPS.

Method

HGGRAPH calculates the points using the HGPREDICT procedure.

References

Lee, Y. & Nelder, J.A. (1996). Hierarchical generalized linear models (with discussion). J. R. Statist. Soc. B, 58, 619-678.

Lee, Y. & Nelder, J.A. (2001). Hierarchical generalized linear models: a synthesis of generalised linear models, random-effect models and structured dispersions. Biometrika, 88, 987-1006.

Lee, Y. & Nelder, J.A. (2006). Double hierarchical generalized linear models (with discussion). Appl. Statist., 55, 139-185.

Lee, Y., Nelder, J.A. & Pawitan, Y. (2006). Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood. Chapman and Hall, Boca Raton.

See also

Procedures: HGANALYSE, HGDISPLAY, HGDRANDOMMODEL, HGFIXEDMODEL, HGFTEST, HGKEEP, HGNONLINEAR, HGPLOT, HGPREDICT, HGRANDOMMODEL, HGRTEST, HGSTATUS, HGTOBITPOISSON, HGWALD.

Commands for: Regression analysis.

Example

CAPTION  'HGGRAPH example',!t(\
         'Breaking angles of cake baked from 3 recipes at 10 temperatures',\
         '(Cochran & Cox, 1957, Experimental Designs, page 300).',\
         'Data values are assumed to follow a GLM with a gamma distribution',\
         'and reciprocal link. The linear predictor contains additional',\
         'random variables, with inverse gamma distributions and reciprocal',\
         'link, for replicates and batches of cake mixture.');\
         STYLE=meta,plain
FACTOR   [NVALUES=270; LEVELS=3] Recipe
&        [LEVELS=15] Replicate
&        [LEVELS=!(175,185...225)] Temperature
GENERATE Recipe,Replicate,Temperature
VARIATE  [NVALUES=270] Angle
READ     Angle
42 46 47 39 53 42 47 29 35 47 57 45 32 32 37 43 45 45
26 32 35 24 39 26 28 30 31 37 41 47 24 22 22 29 35 26
26 23 25 27 33 35 24 33 23 32 31 34 24 27 28 33 34 23
24 33 27 31 30 33 33 39 33 28 33 30 28 31 27 39 35 43
29 28 31 29 37 33 24 40 29 40 40 31 26 28 32 25 37 33
39 46 51 49 55 42 35 46 47 39 52 61 34 30 42 35 42 35
25 26 28 46 37 37 31 30 29 35 40 36 24 29 29 29 24 35
22 25 26 26 29 36 26 23 24 31 27 37 27 26 32 28 32 33
21 24 24 27 37 30 20 27 33 31 28 33 23 28 31 34 31 29
32 35 30 27 35 30 23 25 22 19 21 35 21 21 28 26 27 20
46 44 45 46 48 63 43 43 43 46 47 58 33 24 40 37 41 38
38 41 38 30 36 35 21 25 31 35 33 23 24 33 30 30 37 35
20 21 31 24 30 33 24 23 21 24 21 35 24 18 21 26 28 28
26 28 27 27 35 35 28 25 26 25 38 28 24 30 28 35 33 28
28 29 43 28 33 37 19 22 27 25 25 35 21 28 25 25 31 25 :
FACPRODUCT    !p(Replicate,Recipe); Batch
CALCULATE     xTemperature = Temperature
HGFIXEDMODEL  [DISTRIBUTION=gamma; LINK=reciprocal] Recipe*xTemperature
HGRANDOMMODEL [DISTRIBUTION=inversegamma; LINK=reciprocal] Replicate+Batch
HGANALYSE     Angle
HGGRAPH       xTemperature; GROUPS=Recipe