Evaluation of Binary Classifier Models Using FRESA.CAD

0.0.1 Radar Plots
0.0.2 Feature Analysis

#Model Evaluation

##The Colon Cancer Data Set


ColonData <- read.delim("C:/Users/jtame/Documents/GitHub/FresaTests/DataSets/cancerColonb.txt")
Colon <- ColonData[,-1]
rownames(Colon) <- ColonData[,1]

ExperimentName <- "Colon"
bswimsReps <- 5;
theData <- Colon;
theOutcome <- "Class";
reps <- 5;
fraction <- 0.8;
theData[,1:ncol(theData)] <- sapply(theData,as.numeric)

BSWiMSFileName <- paste(ExperimentName,"BSWIMSMethod.RDATA",sep = "_")
CVFileName <- paste(ExperimentName,"CVMethod.RDATA",sep = "_")

##Benchmarking


BSWiMSMODEL <- BSWiMS.model(formula = paste(theOutcome," ~ 1"),data = theData,NumberofRepeats = bswimsReps)

save(BSWiMSMODEL,file = BSWiMSFileName)

load(file = BSWiMSFileName)

cp <- BinaryBenchmark(theData,theOutcome,reps,fraction)

save(cp,file = CVFileName)


load(file = CVFileName)

##Results

###Classifier Results


hm <- heatMaps(Outcome = "Outcome",data = cp$testPredictions,title = "Heat Map",Scale = TRUE,hCluster = "col",cexRow = 0.25,cexCol = 0.75,srtCol = 45)


#The Times
pander::pander(cp$cpuElapsedTimes)

BSWiMS	RF	RPART	LASSO	SVM	KNN	ENS
9.446	2.366	0.462	0.356	0.016	0.014	12.2

learningTime <- -1*cp$cpuElapsedTimes
pr <- plot(cp)

0.0.1 Radar Plots

op <- par(no.readonly = TRUE)

library(fmsb)
par(mfrow = c(1,2),xpd = TRUE,pty = "s",mar = c(1,1,1,1))

mNames <- names(cp$cpuElapsedTimes)

classRanks <- c(pr$minMaxMetrics$BER[1],pr$minMaxMetrics$ACC[2],pr$minMaxMetrics$AUC[2],pr$minMaxMetrics$SEN[2],pr$minMaxMetrics$SPE[2],min(cp$cpuElapsedTimes))
classRanks <- rbind(classRanks,c(pr$minMaxMetrics$BER[2],0,0,0,0,max(cp$cpuElapsedTimes)))
classRanks <- as.data.frame(rbind(classRanks,cbind(t(pr$metrics[c("BER","ACC","AUC","SEN","SPE"),mNames]),cp$cpuElapsedTimes)))
colnames(classRanks) <- c("BER","ACC","AUC","SEN","SPE","CPU")

classRanks$BER <- -classRanks$BER
classRanks$CPU <- -classRanks$CPU

colors_border = c( rgb(1.0,0.0,0.0,1.0), rgb(0.0,1.0,0.0,1.0) , rgb(0.0,0.0,1.0,1.0), rgb(0.2,0.2,0.0,1.0), rgb(0.0,1.0,1.0,1.0), rgb(1.0,0.0,1.0,1.0), rgb(0.0,0.0,0.0,1.0) )
colors_in = c( rgb(1.0,0.0,0.0,0.05), rgb(0.0,1.0,0.0,0.05) , rgb(0.0,0.0,1.0,0.05),rgb(1.0,1.0,0.0,0.05), rgb(0.0,1.0,1.0,0.05) , rgb(1.0,0.0,1.0,0.05), rgb(0.0,0.0,0.0,0.05) )
radarchart(classRanks,axistype = 0,maxmin = T,pcol = colors_border,pfcol = colors_in,plwd = c(6,2,2,2,2,2,2),plty = 1, cglcol = "grey", cglty = 1,axislabcol = "black",cglwd = 0.8, vlcex  = 0.5 ,title = "Prediction Model")

legend("topleft",legend = rownames(classRanks[-c(1,2),]),bty = "n",pch = 20,col = colors_in,text.col = colors_border,cex = 0.5,pt.cex = 2)


filnames <- c("BSWiMS","LASSO_MIN","RF","IDI","tStudent","kendall","mRMR.classic")

filterRanks <- c(pr$minMaxMetrics$BER[1],pr$minMaxMetrics$ACC[2],pr$minMaxMetrics$AUC[2],pr$minMaxMetrics$SEN[2],pr$minMaxMetrics$SPE[2],max(cp$jaccard),min(cp$featsize));

filterRanks <- rbind(filterRanks,c(pr$minMaxMetrics$BER[2],0,0,0,0,min(cp$jaccard),max(cp$featsize)));


filterRanks <- as.data.frame(rbind(filterRanks,cbind(t(pr$metrics_filter[c("BER","ACC","AUC","SEN","SPE"),filnames]),cp$jaccard[filnames],cp$featsize[filnames])));
colnames(filterRanks) <- c("BER","ACC","AUC","SEN","SPE","Jaccard","SIZE")
filterRanks$BER <- -filterRanks$BER
filterRanks$SIZE <- -filterRanks$SIZE

colors_border = c( rgb(1.0,0.0,0.0,1.0), rgb(0.0,1.0,0.0,1.0) , rgb(0.0,0.0,1.0,1.0), rgb(0.2,0.2,0.0,1.0), rgb(0.0,1.0,1.0,1.0), rgb(1.0,0.0,1.0,1.0), rgb(0.0,0.0,0.0,1.0) )
colors_in = c( rgb(1.0,0.0,0.0,0.05), rgb(0.0,1.0,0.0,0.05) , rgb(0.0,0.0,1.0,0.05),rgb(1.0,1.0,0.0,0.05), rgb(0.0,1.0,1.0,0.05) , rgb(1.0,0.0,1.0,0.05), rgb(0.0,0.0,0.0,0.05) )
radarchart(filterRanks,axistype = 0,maxmin = T,pcol = colors_border,pfcol = colors_in,plwd = c(6,2,2,2,2,2,2),plty = 1, cglcol = "grey", cglty = 1,axislabcol = "black",cglwd = 0.8, vlcex  = 0.6,title = "Filter Method" )


legend("topleft",legend = rownames(filterRanks[-c(1,2),]),bty = "n",pch = 20,col = colors_in,text.col = colors_border,cex = 0.5,pt.cex = 2)


detach("package:fmsb", unload=TRUE)

par(mfrow = c(1,1))
par(op)

0.0.2 Feature Analysis



rm <- rowMeans(cp$featureSelectionFrequency)
selFrequency <- cp$featureSelectionFrequency[rm > 0.1,]
gplots::heatmap.2(as.matrix(selFrequency),trace = "none",mar = c(10,10),main = "Features",cexRow = 0.5)



topFeat <- min(ncol(BSWiMSMODEL$bagging$formulaNetwork),30);
gplots::heatmap.2(BSWiMSMODEL$bagging$formulaNetwork[1:topFeat,1:topFeat],trace="none",mar = c(10,10),main = "B:SWiMS Formula Network")

pander::pander(summary(BSWiMSMODEL$bagging$bagged.model,caption="Colon",round = 3))

coefficients:

Table continues below
	Estimate	lower	OR	upper	u.Accuracy	r.Accuracy
H06524	-0.0005125	0.9994	0.9995	0.9996	0.7446	0.5403
T51493	0.0009451	1.001	1.001	1.001	0.6183	0.6667
H09719	0.001959	1.002	1.002	1.002	0.543	0.7581
R64115	0.0001942	1	1	1	0.6559	0.6828
U09564	0.001763	1.001	1.002	1.002	0.6935	0.7172
J02854	-0.0003363	0.9996	0.9997	0.9997	0.8086	0.6054
Z50753	-0.001888	0.9977	0.9981	0.9985	0.7548	0.7108
L08069	0.0002504	1	1	1	0.586	0.6667
T62947	0.00249	1.002	1.002	1.003	0.703	0.7433
T56604	0.0002423	1	1	1	0.6935	0.7312
U30825	0.001963	1.002	1.002	1.002	0.6753	0.6989
X72727	0.0001356	1	1	1	0.6989	0.7204
H20709	-0.0001287	0.9998	0.9999	0.9999	0.6624	0.6398
R08183	0.0002456	1	1	1	0.7204	0.6703
X14958	0.0004282	1	1	1.001	0.7366	0.6957
D16431	9.193e-05	1	1	1	0.629	0.7957
U14631	-9.399e-05	0.9999	0.9999	0.9999	0.7258	0.5323
D25217	-0.0001172	0.9999	0.9999	0.9999	0.6667	0.6022
X12671	0.0004157	1	1	1	0.7151	0.7312
D14812	0.0003633	1	1	1	0.5394	0.7437
T86444	0.0002764	1	1	1	0.5161	0.8118
X54942	0.0003626	1	1	1	0.6505	0.7312
T41204	0.0005383	1	1.001	1.001	0.5323	0.7258
H78386	-0.001099	0.9986	0.9989	0.9992	0.6237	0.7339
T92451	-0.0001061	0.9999	0.9999	0.9999	0.7935	0.6462
L11706	0.000177	1	1	1	0.6505	0.6613
U28686	0.0004601	1	1	1.001	0.6022	0.6667
X53586	0.0003978	1	1	1.001	0.7097	0.7366
T86473	0.0006366	1	1.001	1.001	0.7258	0.7083
D31885	7.092e-05	1	1	1	0.672	0.7527
X12369	-0.0002737	0.9996	0.9997	0.9998	0.7097	0.707
R84411	0.0002126	1	1	1	0.6864	0.7294
H64489	-8e-05	0.9999	0.9999	0.9999	0.7339	0.6935
U21090	0.0001649	1	1	1	0.7097	0.7204
M36634	-0.0008204	0.999	0.9992	0.9994	0.7462	0.6688
H11084	7.077e-05	1	1	1	0.6452	0.7204
R88740	-0.0001172	0.9998	0.9999	0.9999	0.672	0.7366
M76378.1	-0.0001753	0.9998	0.9998	0.9999	0.8172	0.7043
T47383	-0.0007364	0.999	0.9993	0.9995	0.6478	0.6882
H55916	0.0006002	1	1.001	1.001	0.664	0.7903
T94579	8.9e-05	1	1	1	0.5269	0.8118
T51261	9.528e-05	1	1	1	0.6828	0.6989
H64807	-0.0009621	0.9987	0.999	0.9994	0.6344	0.7177
R44301	-0.000262	0.9996	0.9997	0.9998	0.7204	0.6452
T61661	-0.0001023	0.9999	0.9999	0.9999	0.681	0.7079
R67343	-0.000618	0.9992	0.9994	0.9996	0.6855	0.6855
M22382	0.0002529	1	1	1	0.7581	0.7742
T71025	-0.0001647	0.9998	0.9998	0.9999	0.7677	0.6989
R54097	0.0004602	1	1	1.001	0.6048	0.8038
M80815	-0.000895	0.9988	0.9991	0.9994	0.7245	0.7043
X63629	0.001868	1.001	1.002	1.003	0.7774	0.786
J05032	0.001288	1.001	1.001	1.002	0.7011	0.7667
J04102	0.0002824	1	1	1	0.6344	0.7366
M76378.2	-0.0002113	0.9997	0.9998	0.9999	0.8022	0.7645
T61661.1	-2.964e-05	1	1	1	0.6505	0.7258
M63391	-7.888e-05	0.9999	0.9999	0.9999	0.8527	0.7548
M76378	-0.0001392	0.9998	0.9999	0.9999	0.8161	0.729
R36977	0.001039	1.001	1.001	1.001	0.7441	0.8366
R87126	-0.0003403	0.9995	0.9997	0.9998	0.829	0.7753
M26697	1.646e-05	1	1	1	0.7043	0.7312
M35878	0.0001967	1	1	1	0.5484	0.7957
Z49269	-8.413e-05	0.9999	0.9999	0.9999	0.6989	0.6828
H43887	-0.0001385	0.9998	0.9999	0.9999	0.7441	0.7086
M94132	-1.932e-05	1	1	1	0.6747	0.6855
U25138	-0.0001469	0.9998	0.9999	0.9999	0.7634	0.672
M64110	-5.604e-05	0.9999	0.9999	1	0.7204	0.7312
T67077	-0.0002232	0.9997	0.9998	0.9999	0.7312	0.6882
H40095	0.0001929	1	1	1	0.7247	0.771
T47377	0.0001805	1	1	1	0.729	0.7882
H08393	0.002531	1.001	1.003	1.004	0.7817	0.8344
T60155	-1.133e-05	1	1	1	0.7742	0.6828

Table continues below
	full.Accuracy	u.AUC	r.AUC	full.AUC	IDI	NRI
H06524	0.8952	0.7134	0.5687	0.9068	0.6243	1.717
T51493	0.8978	0.6428	0.6496	0.897	0.5492	1.533
H09719	0.9301	0.5742	0.7545	0.9356	0.5446	1.8
R64115	0.8387	0.6754	0.6723	0.858	0.5462	1.467
U09564	0.8753	0.7175	0.6867	0.8829	0.4954	1.363
J02854	0.886	0.7726	0.6246	0.8871	0.4758	1.437
Z50753	0.8968	0.7405	0.7315	0.8995	0.4172	1.413
L08069	0.8333	0.628	0.6496	0.8367	0.4904	1.3
T62947	0.8535	0.7204	0.7175	0.8549	0.4437	1.342
T56604	0.8387	0.7216	0.7235	0.8477	0.426	1.367
U30825	0.8505	0.6992	0.6814	0.8569	0.4282	1.3
X72727	0.828	0.7189	0.7049	0.8428	0.4269	1.233
H20709	0.8677	0.6504	0.6663	0.8695	0.4305	1.293
R08183	0.8477	0.7333	0.6649	0.8649	0.4138	1.294
X14958	0.8656	0.7624	0.6653	0.8727	0.3905	1.253
D16431	0.9194	0.6511	0.7735	0.917	0.3459	1.25
U14631	0.8333	0.6989	0.5455	0.847	0.3786	1.317
D25217	0.8333	0.6633	0.6337	0.8265	0.4046	1.167
X12671	0.8656	0.7383	0.7058	0.8754	0.3842	1.187
D14812	0.8943	0.5703	0.7116	0.9033	0.3948	1.239
T86444	0.9247	0.5432	0.7758	0.9314	0.3719	1.417
X54942	0.8441	0.6814	0.6877	0.8468	0.3742	1.183
T41204	0.8333	0.5455	0.6989	0.847	0.3641	1.333
H78386	0.8844	0.5839	0.7631	0.89	0.3588	1.467
T92451	0.8774	0.7684	0.6549	0.8777	0.3604	1.237
L11706	0.8817	0.6712	0.6489	0.8674	0.3854	1.233
U28686	0.8333	0.6337	0.6633	0.8265	0.3825	1.3
X53586	0.9086	0.7307	0.7277	0.9155	0.3585	1.383
T86473	0.8374	0.7457	0.6768	0.8475	0.3419	1.087
D31885	0.8548	0.6811	0.7231	0.8534	0.3527	1.317
X12369	0.8723	0.6864	0.7303	0.8789	0.34	1.35
R84411	0.7939	0.691	0.7085	0.8153	0.3415	1.067
H64489	0.8763	0.7051	0.7173	0.8837	0.3069	1.317
U21090	0.828	0.7307	0.7049	0.8462	0.3141	1.117
M36634	0.857	0.7133	0.6888	0.8605	0.2914	1.177
H11084	0.8602	0.6807	0.6913	0.8644	0.2677	1.083
R88740	0.8387	0.6436	0.7515	0.8477	0.2947	1.15
M76378.1	0.8591	0.7765	0.7272	0.8561	0.2917	1.183
T47383	0.8575	0.6129	0.7106	0.8589	0.3127	1.233
H55916	0.8817	0.6509	0.7659	0.8794	0.2858	0.8083
T94579	0.871	0.5311	0.7826	0.8659	0.2925	1.233
T51261	0.8226	0.7098	0.6644	0.8352	0.2976	0.9667
H64807	0.8172	0.6263	0.7438	0.8259	0.2899	0.925
R44301	0.8602	0.6913	0.6807	0.8644	0.2535	1.017
T61661	0.8369	0.6823	0.7122	0.8486	0.2885	1.161
R67343	0.8414	0.671	0.7068	0.8566	0.2839	1.1
M22382	0.8366	0.7777	0.72	0.8413	0.2707	1.057
T71025	0.8559	0.7641	0.7251	0.8563	0.2656	1.203
R54097	0.8817	0.6324	0.7644	0.8845	0.2749	1.225
M80815	0.836	0.7132	0.724	0.8422	0.2614	1.062
X63629	0.8763	0.79	0.7578	0.8735	0.2695	1.093
J05032	0.8581	0.7179	0.7455	0.8566	0.249	0.9833
J04102	0.8387	0.6417	0.7004	0.8477	0.2376	0.85
M76378.2	0.8624	0.7662	0.7827	0.8592	0.2455	0.95
T61661.1	0.8333	0.6269	0.7466	0.8606	0.2289	0.95
M63391	0.8742	0.8252	0.782	0.8793	0.2407	1.26
M76378	0.8495	0.7805	0.7559	0.8465	0.2236	0.8933
R36977	0.8785	0.7758	0.8106	0.8847	0.2318	0.8633
R87126	0.8806	0.813	0.7904	0.8782	0.2441	1.237
M26697	0.8011	0.7197	0.7235	0.8015	0.2399	0.75
M35878	0.871	0.575	0.7633	0.8591	0.2086	1.033
Z49269	0.8226	0.6644	0.7098	0.8352	0.2236	1.133
H43887	0.8387	0.7117	0.7244	0.8464	0.2057	1.027
M94132	0.8387	0.6405	0.7153	0.8494	0.2094	0.8667
U25138	0.8387	0.7212	0.6947	0.8375	0.206	1.017
M64110	0.8333	0.6811	0.7473	0.8402	0.2002	0.8833
T67077	0.8011	0.703	0.6902	0.8254	0.1994	1.067
H40095	0.843	0.7594	0.7461	0.8456	0.1927	0.7467
T47377	0.8452	0.7477	0.7547	0.8377	0.1883	0.8967
H08393	0.8806	0.7954	0.8151	0.8768	0.1994	1.013
T60155	0.7796	0.7432	0.6996	0.8087	0.1799	1.033

	z.IDI	z.NRI	Frequency
H06524	12.07	15.66	0.4
T51493	10.3	11	0.2
H09719	9.901	18.87	0.2
R64115	9.893	11.38	0.2
U09564	9.334	9.486	1
J02854	9.032	10.48	1
Z50753	8.779	12.27	1
L08069	8.508	7.855	0.2
T62947	8.245	8.978	0.8
T56604	8.099	9.687	0.2
U30825	7.996	8.785	1
X72727	7.894	7.254	0.2
H20709	7.78	8.027	1
R08183	7.737	8.208	0.6
X14958	7.702	8.286	1
D16431	7.367	7.497	0.2
U14631	7.358	9.073	0.2
D25217	7.337	6.761	0.2
X12671	7.331	7.329	1
D14812	7.331	7.544	0.6
T86444	7.315	9.11	0.2
X54942	7.198	7.431	0.4
T41204	7.15	8.421	0.2
H78386	7.15	9.983	0.4
T92451	7.124	7.665	1
L11706	7.015	7.208	0.2
U28686	6.979	7.747	0.2
X53586	6.835	8.911	0.2
T86473	6.77	6.668	0.8
D31885	6.722	7.898	0.2
X12369	6.605	8.768	0.8
R84411	6.342	5.999	0.6
H64489	6.306	8.879	0.8
U21090	6.098	6.427	0.2
M36634	6.046	7.368	1
H11084	6.029	6.442	0.2
R88740	5.999	6.648	0.2
M76378.1	5.975	7.345	1
T47383	5.969	7.311	0.4
H55916	5.926	3.999	0.4
T94579	5.909	7.764	0.2
T51261	5.876	5.348	0.2
H64807	5.868	5.169	0.4
R44301	5.739	5.575	0.2
T61661	5.729	6.695	0.6
R67343	5.607	6.361	0.4
M22382	5.567	6.435	1
T71025	5.537	7.329	1
R54097	5.457	7.182	0.4
M80815	5.448	6.19	0.8
X63629	5.392	6.989	1
J05032	5.281	5.256	1
J04102	5.236	4.242	0.2
M76378.2	5.059	5.432	1
T61661.1	5.033	5.317	0.2
M63391	5.022	8.509	1
M76378	4.995	5.139	1
R36977	4.98	4.596	1
R87126	4.969	7.773	1
M26697	4.888	3.702	0.2
M35878	4.828	5.536	0.2
Z49269	4.825	6.44	0.2
H43887	4.812	6.023	1
M94132	4.769	4.725	0.4
U25138	4.648	5.912	0.2
M64110	4.569	4.855	0.2
T67077	4.527	5.925	0.2
H40095	4.405	4.134	1
T47377	4.342	4.707	1
H08393	4.275	6.074	1
T60155	4.204	5.559	0.2

Accuracy: 0.9032
tAUC: 0.9045
sensitivity: 0.9
specificity: 0.9091
bootstrap:



hm <- heatMaps(Outcome = theOutcome,data = theData[,c(theOutcome,rownames(selFrequency))],title = "Heat Map",Scale = TRUE,hCluster = "col",cexRow = 0.25,cexCol = 0.75,srtCol = 45)


vlist <- rownames(selFrequency)
vlist <- cbind(vlist,vlist)
univ <- univariateRankVariables(variableList = vlist,formula = paste(theOutcome,"~1"),Outcome = theOutcome,data = theData,type = "LOGIT",rankingTest = "zIDI",uniType = "Binary")[,c("controlMean","controlStd","caseMean","caseStd","ROCAUC","WilcoxRes.p")]

100 : H15813 200 : M65105


cnames <- colnames(univ);
univ <- cbind(univ,rm[rownames(univ)])
colnames(univ) <- c(cnames,"Frequency")
univ <- univ[order(-univ[,5]),]
pander::pander(univ[1:topFeat,],caption = "Features",round = 4)

Features (continued below)
	controlMean	controlStd	caseMean	caseStd	ROCAUC
R87126	806.5	546.1	271.7	185.5	0.8841
H08393	55.01	24.97	132.6	80.18	0.875
R36977	125.7	63.3	375.6	340.1	0.8648
M22382	405.2	220.3	1142	868.5	0.8648
M26383	114.9	168.6	398.1	475.6	0.8534
H40095	319.1	215.5	800.5	529.5	0.8409
X63629	57.35	31.71	154.8	108.2	0.8352
J05032	81.3	55.47	194.7	120.5	0.833
X12671	333.3	263.5	850.5	582.4	0.8295
Z50753	447.6	216.3	233.9	119	0.8284
J02854	907.3	682.6	222.9	266.8	0.8261
U09564	116.4	63.94	262.9	176.3	0.8239
H43887	850.5	547.3	330.4	414.5	0.8216
M63391	2303	1538	597.1	568.4	0.8205
M76378.2	1052	844.1	260.3	172	0.8136
M36634	214.5	146.9	93.32	96.29	0.8125
T86473	156.4	94.12	407	323.7	0.8114
X14958	350.8	209.1	716.1	434.5	0.8102
M76378	1283	798.5	465.9	357.5	0.8068
T47377	259.1	265.6	930.2	813.4	0.8057
M26697	852.3	478.3	1848	1101	0.8023
R84411	338.9	225.6	747.4	483.9	0.7989
T71025	1892	697.2	1103	675.2	0.7977
X54942	123	86.76	337.1	299.6	0.7932
R08183	356.8	248.3	840.3	593.4	0.7932
M76378.1	1306	805.3	490.9	375.2	0.792
D31885	354.3	252.2	768.2	563.3	0.7886
H06524	362.9	272.6	144.6	183	0.7875
X55715	851.7	464.2	1555	833.8	0.7852
H77597	777.6	691	356.3	407.9	0.7841

	WilcoxRes.p	Frequency
R87126	0	0.64
H08393	0	0.52
R36977	0	0.46
M22382	0	0.46
M26383	1e-04	0.72
H40095	0	0.32
X63629	0	0.62
J05032	0	0.44
X12671	0	0.3
Z50753	0	0.52
J02854	0	0.36
U09564	0	0.16
H43887	0	0.52
M63391	0	0.58
M76378.2	0	0.48
M36634	0	0.2
T86473	0	0.2
X14958	0	0.18
M76378	0	0.34
T47377	1e-04	0.6
M26697	1e-04	0.2
R84411	1e-04	0.28
T71025	0	0.64
X54942	1e-04	0.2
R08183	1e-04	0.42
M76378.1	0	0.3
D31885	2e-04	0.12
H06524	1e-04	0.14
X55715	2e-04	0.12
H77597	2e-04	0.22

Evaluation of Binary Classifier Models Using FRESA.CAD

José Tamez-Peña

Nov 2, 2018

0.0.1 Radar Plots

0.0.2 Feature Analysis