Rでの因果グラフの描き方
Rで描くグラフは統計分析のグラフに留まらない。有向非巡回グラフ (DAG ; Directed Acyclic Graph)もRで描く事が出来る。
Webブラウザ上でDAGを描いて分析する事も出来る。
install.packages ("DiagrammeR" )library (DiagrammeR)
grViz (" digraph dag_1s { x -> y } " )
grViz (" digraph dag_1a { x[shape = box, label = <<I>x</I>>] y[shape = box, label = <<I>y</I>>] x -> y[label = <<I> β₁</I>>] } " )
grViz (" digraph dag_2 { graph [rankdir = TB, nodesep = 1.0, label = 'common cause'] edge [arrowsize = .5] x[shape = box, label = <<I>x</I>>, width = .2, height = .2] y[shape = box, label = <<I>y</I>>, width = .2, height = .2] z[shape = circle, label = <<I>z</I>>, width = .15, height = .15] x -> y[style = dashed] z -> x z -> y { rank = same; x; y; } } " )
grViz (" digraph dag_3 { graph [rankdir = TB, nodesep = 1.0, label = 'mediator'] edge [arrowsize = .5] x[shape = box, label = <<I>x</I>>, width = .2, height = .2] y[shape = box, label = <<I>y</I>>, width = .2, height = .2] z[shape = circle, label = <<I>z</I>>, width = .15, height = .15] x -> y[style = dashed] x -> z z -> y { rank = same; x; y; } { rank = max; x; y; } } " )
grViz (" digraph EFA { graph [rankdir = TB, label = <<I>Exploratory Factor Analysis</I>>, labelloc = t]; factor1[label = <factor₁>]; factor2[label = <factor₂>]; var1[shape=box, label = <var₁>]; var2[shape=box, label = <var₂>]; var3[shape=box, label = <var₃>]; var4[shape=box, label = <var₄>]; var5[shape=box, label = <var₅>]; var6[shape=box, label = <var₆>]; e1[shape=none, label = <e₁>]; e2[shape=none, label = <e₂>]; e3[shape=none, label = <e₃>]; e4[shape=none, label = <e₄>]; e5[shape=none, label = <e₅>]; e6[shape=none, label = <e₆>]; factor1 -> var1; factor1 -> var2; factor1 -> var3; factor1 -> var4; factor1 -> var5; factor1 -> var6; factor2 -> var1; factor2 -> var2; factor2 -> var3; factor2 -> var4; factor2 -> var5; factor2 -> var6; e1 -> var1 e2 -> var2 e3 -> var3 e4 -> var4 e5 -> var5 e6 -> var6 { rank = same; factor1; factor2; } { rank = same; var1; var2; var3; var4; var5; var6; } { rank = same; e1; e2; e3; e4; e5; e6; } { rank = max; e1; e2; e3; e4; e5; e6; } }" )
grViz (" digraph PCA { graph [label = <<I>Principal Component Analysis</I>>, labelloc = t ]; var1[shape=box, label = <var₁>]; var2[shape=box, label = <var₂>]; var3[shape=box, label = <var₃>]; var4[shape=box, label = <var₄>]; var5[shape=box, label = <var₅>]; var6[shape=box, label = <var₆>]; pc1[label = <principal component₁>]; pc2[label = <principal component₂>]; var1 -> pc1; var2 -> pc1; var3 -> pc1; var4 -> pc1; var5 -> pc1; var6 -> pc1; var1 -> pc2; var2 -> pc2; var3 -> pc2; var4 -> pc2; var5 -> pc2; var6 -> pc2; }" )
grViz (" digraph PCE { graph [layout = neato, fontname='times-italic', splines = true, label ='Partial Correlation Coefficient', labelloc = t]; node [fontname='times-italic']; z[pos = '3,4!']; x[shape=box, pos = '2,3!']; y[shape=box, pos = '4,3!']; ex[shape=none; label=<e<sub>x</sub>>; pos = '2,2!']; ey[shape=none; label=<e<sub>y</sub>>; pos = '4,2!']; z -> x; z -> y; ex -> x; ey -> y; ex -> ey[color = red, headlabel = <<I>r<SUB>xy|z</SUB></I>>, dir = both, labeldistance = '4.5']; } " )
grViz (" digraph MRA { graph [label = 'Multiple Regression Analysis', labelloc = b ]; layout = neato y[pos = '5.0, 3.0!', label = <<I>y</I>>] x1[pos = '3.0, 4.0!', label = <<I>x</I>₁>] x2[pos = '2.0, 3.4!', label = <<I>x</I>₂>] x3[pos = '2.0, 2.6!', label = <<I>x</I>₃>] x4[pos = '3.0, 2.0!', label = <<I>x</I>₄>] x1 -> y[taillabel = <<I>β₁</I>>, labeldistance = 2] x2 -> y[taillabel = <<I>β₂</I>>, labeldistance = 3] x3 -> y[taillabel = <<I>β₃</I>>, labeldistance = 3] x4 -> y[taillabel = <<I>β₄</I>>, labeldistance = 3] } " )
grViz (" digraph PATHD { graph [label = 'Path Diagram', labelloc = b ]; layout = neato y1[pos = '4.5, 2.5!', label = <<I>y</I>₁>] y2[pos = '5.0, 1.0!', label = <<I>y</I>₂>] x1[pos = '3.5, 4.0!', label = <<I>x</I>₁>] x2[pos = '3.2, 3.0!', label = <<I>x</I>₂>] x3[pos = '2.0, 2.5!', label = <<I>x</I>₃>] x4[pos = '2.0, 1.0!', label = <<I>x</I>₄>] x1 -> y1[headlabel = <<I>α₁₁</I>>, labeldistance = 4] x1 -> x3[headlabel = <<I>γ₁₃</I>>, labeldistance = 4] x2 -> y1[headlabel = <<I>α₂₁</I>>, labeldistance = 3] x2 -> y2[headlabel = <<I>β₂₂</I>>, labeldistance = 4] x3 -> y1[headlabel = <<I>α₃₁</I>>, labeldistance = 2] x3 -> y2[headlabel = <<I>β₃₂</I>>, labeldistance = 3] x4 -> y2[headlabel = <<I>β₄₂</I>>, labeldistance = 2] y1 -> y2[headlabel = <<I>β₁₂</I>>, labeldistance = 5] } " )
ggdagによる分析
単にパス図を描くだけではなく，グラフを用いて分析を行うのがDAGの本来の使用法である。
install.packages ("ggdag" )library (ggdag)library (dagitty)
細かく好みのグラフを描く道具ではなく，グラフを用いて分析のアドヴァイスを示す為の道具と言える。
<- dagitty ("dag{ x <- z -> y x -> y x[exposure] y[outcome] }" )<- tidy_dagitty (dag01)ggdag (ggdag01)ggdag_adjustment_set (ggdag01)
<- dagitty ("dag{ x -> m -> y x -> y x[exposure] y[outcome] }" )<- tidy_dagitty (dag02)ggdag (ggdag02) + theme_dag ()ggdag_adjustment_set (ggdag02) + theme_dag ()
<- dagitty ("dag{ x <- z -> y x -> y ex -> x ey -> y ex <-> ey ex[unobserved] ey[unobserved] }" )<- tidy_dagitty (dag03)ggdag (ggdag03) + theme_dag_grid () + theme_dag_grid ()
グラフによる分析
<- dagitty ("dag{ x <- z -> y x -> m -> y p -> x -> y p -> z p -> m }" )<- tidy_dagitty (dag10)ggdag (ggdag10) + theme_dag_grid ()
ggdag_ancestors (ggdag10, "m" )ggdag_parents (ggdag10, "m" )
ggdag_descendants (ggdag10, "z" )ggdag_children (ggdag10, "z" )
ggdag_exogenous (ggdag10) + theme_dag_gray ()
ggdag_collider (ggdag10) + theme_dag_gray_grid ()
ggdag_adjustment_set (ggdag10, exposure = "x" , outcome = "y" , effect = "total" )
ggdag_adjustment_set (ggdag10, exposure = "x" , outcome = "y" , effect = "direct" )
