Multivariate Analysis in the Characterization and Classification of Soils

Abstract

Soil is a fundamental natural resource in the balance for the ecosystems as well as for agriculture, food, and housing. The soil is very susceptible to changes in its structure due to contamination or degradation of anthropogenic origin. Therefore, its evaluation, whether for environmental purposes or as an agricultural or housing resource, must be carried out in depth. This evaluation comprises the analysis of multiple physical, physicochemical and chemical-biological parameters. However, due to these multiple parameters, the use of multivariate statistical methods becomes necessary. In this chapter, the soil data analysis was performed by the method of Principal Components Analysis for a reduction of dimensions and, to carry out a better interpretation of results. This method was applied to carry out a characterization and classification of soil samples. The analysis was performed with data obtained from soil samples from the Bolivian Altiplano. The results show the potential of the principal component of the method in processing data.

1. Introduction

Soil and water are fundamental natural resources in the balance of ecosystems as well as in agriculture, food, and housing being thus fundamental for life.

Soils are composed of two environments, biotic and abiotic. The first constituted of microorganisms while the second, abiotic, is composed of solid, liquid and gaseous phases. The two environments characterize a particular soil giving it its uniqueness.

Soil and natural waters are highly susceptible to big changes in their structure and composition due to anthropogenic degradation or contamination. Therefore, its evaluation, whether for environmental purposes or as agricultural or housing resources, must be carried out deeply. This evaluation comprises the analysis of multiple physical, physicochemical and chemical-biological parameters. For example, to know the fertility of the soils, it is important to analyze parameters such as: pH, Electrical Conductivity, Organic Matter, exchangeable cations and others. The evaluations are carried out by comparison of these parameters with values established in agricultural or environmental regulations. However, due to complexity and variety and a big number of parameters, its analysis may become tough. Because of this, the use of multivariate statistical methods becomes imperative. Thus, the multivariate analysis applied to the characterization and classification of soils and natural waters according to the field of study that is intended to be carried out, grows up in importance.

The Principal Components Analysis offers us an alternative for the characterization and classification of soils. The different soil samples or soil sampling points constitute the elements of a system, and the physicochemical parameters measured in these samples, the variables. Thus, we have a system with multiple elements and variables since generally, the sampling points and the variables are numerous. The data analysis can be quite complex because the representative points among the sampling points should be represented in multidimensional spaces. Even though the variables could be represented in one-dimensional (considering each variable) or two-dimensional (every two variables) spaces, this is neither practical nor objectively informative.

The analysis through Principal Components with reduction of dimensions offers us precisely an alternative. Since the set of multivariables can be reduced to a few compound variables, the analysis becomes feasible and, the conclusions are more objective.

However, not all data sets are susceptible to Principal Component Analysis (PCA). They must meet certain requirements, for example they should be comprised of numerical variables and, the correlations between the variables must be above an acceptable level. If these requirements are not met, although a PCA could be made, their results would not be valid. The compliance for these requirements is given by the correlation matrix, where correlations must be observed. The Kaiser-Meyer-Olkin Measure (KMO) of sampling adequacy is a statistic that indicates the amount of variance in the variables that can be explained with the PCA. It is somewhat similar to the coefficient of determination R² from a linear regression analysis. Kaiser proposed the following criteria for KMO [1]:

1. 0.9≤KMO≤1.0 = Excellent sample adequacy.

2. 0.8≤KMO≤0.9 = Good sample adequacy.

3. 0.7≤KMO≤0.8 = Acceptable sample adequacy.

4. 0.6≤KMO≤0.7 = Regular sample adequacy.

5. 0.5≤KMO≤0.6 = Bad sample adequacy.

6. 0.0≤KMO≤0.5 = Unacceptable sample adequacy.

Therefore, the KMO is required to be a value, at least, greater than 0.7 for the PCA to be acceptable. Bartlett’s test of sphericity is a statistical test which null hypothesis is an identity matrix. The acceptance of the null hypothesis means that there are no correlations (Sig. > 0.05). On the other hand, the alternative hypothesis is a non-identity matrix. The acceptance of this hypothesis means that there are correlations (Sig. < 0.05) and thus, a PCA can be performed. The statistical evaluation was made by SPSS Software.

2. PCA in the analysis of soil samples

In a study carried out by Ramos Ramos et al. [2], water samples from the Bolivian altiplano were analyzed. The results of various elements and variables determined in the water are presented in Table 1.

Location	Sample ID	Water type	EC (μS/cm)	pH	Eh (mV)	${\mathrm{HCO}}_3^{-}$ (mg/L)	F; (mg/L)	${\mathrm{Cl}}^{-}$ (mg/L)	${{\mathrm{SO}}_4}^{2-}$ (mg/L)	${\mathrm{Ca}}^{2+}$; (mg/L)	${\mathrm{Mg}}^{2+}$ (mg/L)	${\mathrm{Na}}^{+}$; (mg/L)	${\mathrm{K}}^{+}$ (mg/L)	Ionic balance (%)
Cayhuasi	CAP1	Mg–Na–Ca–${\mathrm{HCO}}_3$–${\mathrm{SO}}_4$	1,120	7.45	167	561.4	0.01	13.5	170.8	69.8	85 5	80.5	14.3	4.1
Soracachi 1	SOP1	Mg–Ca–Na–${\mathrm{HCO}}_3$–${\mathrm{SO}}_4$	912	7.33	165	427.1	0.24	19.7	145.4	55.1	62.3	56.8	6.1	–1.0
Soracachi 2	SOP2	Mg–Na–Ca–${\mathrm{HCO}}_3$–${\mathrm{SO}}_4$	936	7.15	184	417.4	0.01	21.0	158.8	56.3	64.8	67.6	5.0	1.4
Paria	PAP1	Na–Mg–${\mathrm{HCO}}_3$–Cl–${\mathrm{SO}}_4$	2,120	7.41	173	717.6	1.04	198.2	242.8	72.5	58.6	291.5	42.1	–0.7
Chusaqueri	CHP1	Ca–Na–Cl	1,480	7.52	160	153.8	0.03	294.9	85.6	156.3	20.4	88.3	8.2	1.9
Toledo 1	TOP1	Na–Ca–Cl–${\mathrm{HCO}}_3$	1,400	7.72	154	270.9	0.01	233.0	90.4	68.8	15.4	183.5	30.4	0.5
Toledo 2	TOP2	Na–Ca–Cl	3,860	7.38	170	263.6	0.01	926.7	183.3	206.9	55.4	421.0	28.0	–0.9
Kulliri	KUP1	Na–${\mathrm{HCO}}_3$–B–${\mathrm{SO}}_4$	850	7.75	160	297.8	0.11	61.9	97.0	27.2	3.4	135.0	19.1	–4.3
Copacabanita	COP1	Ca–Na–${\mathrm{SO}}_4$	1,390	7.08	190	190.4	0.47	25.5	562.5	234.5	16.4	125.5	6.9	8.6
Tolaloma	TOLP1	Ca–${\mathrm{HCO}}_3$–${\mathrm{SO}}_4$	660	7.61	158	266.0	0.01	26.8	105.6	98.7	11.1	33.0	6.9	0.7
Andamarca	ANP1	Na–Ca–${\mathrm{HCO}}_3$–${\mathrm{SO}}_4$	1,190	7.69	169	483.3	0.01	74.1	142.8	114.7	13.1	179.0	18.5	7.3
Avaroa	AVP1	Ca–Na–${\mathrm{HCO}}_3$	590	7.29	169	290.4	0.19	14.1	48.0	72.3	7.4	49.2	5.2	2.3
Pampa Aullagas	PAMP1	Na–Ca–Cl–${\mathrm{HCO}}_3$–${\mathrm{SO}}_4$	1,360	6.41	218	219.7	0.35	164.5	144.2	69.9	22.4	137.0	26.7	1.0
Quillacas 1	QUP1	Na–B–Cl–${\mathrm{HCO}}_3$	1,200	7.90	141	234.3	0.26	189.7	79.1	36.2	6.7	175.0	16.6	–2.3
Quillacas 2	QUP2	Na–Cl	810	6.55	210	61.0	0.20	93.7	66.8	11.5	4.9	123.8	21.4	–2.0
Quillacas 3	QUP3	Na–Cl–B–${\mathrm{SO}}_4$	410	6.74	205	36.6	0.13	35.9	36.8	10.0	3.6	44.6	17.5	7.0
Condo K2	CONP2	Na–Ca–${\mathrm{HCO}}_3$	660	7.55	162	234.3	0.32	42.0	55.6	52.0	8.2	109.4	9.9	13.0
Condo K4	CONP4	Na–Ca–${\mathrm{HCO}}_3$–B	570	7.55	165	227.0	0.29	30.4	48.7	43.1	7.4	51.0	8.9	–3.9
Caraynacha	CARP1	Ca–Na–${\mathrm{HCO}}_3$	400	7.48	168	172.1	0.13	20.9	30.5	42.9	6.2	44.4	13.9	9.6
Llapallapani	LLAP1	Na–Ca–${\mathrm{SO}}_4$–${\mathrm{HCO}}_3$	210	6.97	195	43.9	0.05	7.1	40.1	11.5	4.3	14.6	6.2	–3.0
Challapata	CHAP1	Ca–Na–Mg–${\mathrm{HCO}}_3$–CI	650	6.84	197	135.5	0.15	47.0	35.7	55.3	15.3	44.3	6.5	10.0
Huancane	HUAP1	Na–Ca–${\mathrm{HCO}}_3$–Cl	870	7.13	185	292.9	0.14	78.8	46.7	70.1	13.8	130.5	7.2	13.0
Irukasa	IRP1	Na–Cl	4,630	7.35	173	593.1	0.01	1,219.7	9.1	39.6	7.2	1,333	26.9	16.1
Realenga	REP1	Na–Ca–Mg–${\mathrm{SO}}_4$–${\mathrm{HCO}}_3$	770	6.81	206	178.2	0.30	37.1	176.6	56.0	23.1	101.0	5.8	8.9
Pazña	PAZP2	Na–Ca–${\mathrm{SO}}_4$–${\mathrm{HCO}}_3$	1,270	7.19	180	300.2	0.67	72.1	282.6	114.3	20.5	211.5	23.6	14.3
Totoral	TOTP1	Na–Cl–${\mathrm{NO}}_3$–${\mathrm{SO}}_4$	1,450	6.87	198	98.8	0.55	168.8	131.1	51.3	10.4	208.0	22.8	0.5
Cayumalliri	CAYP1	Ca–Na–${\mathrm{HCO}}_3$–${\mathrm{SO}}_4$	640	6.70	212	205.0	0.07	33.9	72.1	64.5	15.1	35.0	3.0	–1.1
Sora Sora	SORP1	Al–Ca–Mg–${\mathrm{SO}}_4$	4,500	3.79	378	0.0	4.06	28.1	1,020.2	130.7	63.6	45.5	6.7	1.6
Chapana^r	CHAO1	Ca–Mg–Na–${\mathrm{HCO}}_3$–${\mathrm{SO}}_4$	280	7.60	157	109.8	0.01	9.5	44.2	20.8	8.8	16.4	3.9	–7.7
Totoral^r	TOR1	Ca–${\mathrm{SO}}_4$	2,580	3.88	369	0.0	0.51	104.0	1,546.9	333.5	40.4	28.2	9.2	–2.1
Avicaya^r	AVR1	Ca–${\mathrm{SO}}_4$	2,530	3.10	417	0.0	1.09	106.9	1,261.1	255.3	36.8	56.7	6.6	–2.1
Pazna^r	PAZR1	Ca–Na–${\mathrm{SO}}_4$	1,960	4.71	221	14.6	0.06	151.7	874.9	191.3	36.2	128.5	12.0	3.3

Table 1.

Major ion composition in ground and surface water samples in the Poopó basin from the Bolivian Altiplano.

Below detection limit.

Samples ID end P pertain to wells.

Samples ID end R pertain to rivers.

Reproduced with permission from Springer Nature; Excerpt from [2].

Table 2 shows the correlation matrix of parameters. It can be seen that there are correlations between different variables, which is an indicative of underlying structures. In principle, a PCA would be feasible.

Correlaciones
		EC	pH	Eh	HCO3	F	Cl	SO4	Ca	Mg	Na	K
EC	Pearson correlation	1	−.287	.429*	.091	.531**	.709**	.505**	.493**	.419*	.625**	.342
	sig. (2-tailed)		.112	.014	.620	.002	.000	.003	.004	.017	.000	.055
	N	32	32	32	32	32	32	32	32	32	32	32
pH	Pearson correlation	−.287	1	−.569**	.378*	−.393*	.120	−.624**	−.361*	−.109	.133	.102
	sig. (2-tailed)	.112		.001	.033	.026	.514	.000	.043	.554	.468	.580
	N	32	32	32	32	32	32	32	32	32	32	32
Eh	Pearson correlation	.429*	−.569**	1	−.462**	.582**	−.107	.815**	.569**	.276	−.145	−.325
	sig. (2-tailed)	.014	.001		.008	.000	.559	.000	.001	.126	.428	.070
	N	32	32	32	32	32	32	32	32	32	32	32
HCO3	Pearson correlation	.091	.378*	−.462**	1	−.228	.307	−.415*	−.262	.313	.475**	.456**
	sig. (2-tailed)	.620	.033	.008		.210	.087	.018	.148	.081	.006	.009
	N	32	32	32	32	32	32	32	32	32	32	32
F	Pearson correlation	.531**	−.393*	.582**	−.228	1	−.128	.523**	.225	.358*	−.098	−.033
	sig. (2-tailed)	.002	.026	.000	.210		.486	.002	.215	.044	.594	.860
	N	32	32	32	32	32	32	32	32	32	32	32
Cl	Pearson correlation	.709**	.120	−.107	.307	−.128	1	−.085	.123	.033	.897**	.497**
	sig. (2-tailed)	.000	.514	.559	.087	.486		.643	.501	.857	.000	.004
	N	32	32	32	32	32	32	32	32	32	32	32
SO4	Pearson correlation	.505**	−.624**	.815**	−.415*	.523**	−.085	1	.832**	.400*	−.151	−.171
	sig. (2-tailed)	.003	.000	.000	.018	.002	.643		.000	.023	.408	.350
	N	32	32	32	32	32	32	32	32	32	32	32
Ca	Pearson correlation	.493**	−.36l*	.569**	−.262	.225	.123	.832**	1	.353*	−.057	−.107
	sig. (2-tailed)	.004	.043	.001	.148	.215	.501	.000		.048	.756	.559
	N	32	32	32	32	32	32	32	32	32	32	32
Mg	Pearson correlation	.419*	−.109	.276	.313	.358*	.033	.400*	.353*	1	−.060	.063
	sig. (2-tailed)	.017	.554	.126	.081	.044	.857	.023	.048		.746	.733
	N	32	32	32	32	32	32	32	32	32	32	32
Na	Pearson correlation	.625**	.133	−.145	.475**	−.098	.897**	.151	−.057	−.060	1	.512**
	sig. (2-tailed)	.000	.468	.428	.006	.594	.000	.408	.756	.746		.003
	N	32	32	32	32	32	32	32	32	32	32	32
K	Pearson correlation	.342	.102	−.325	.456**	−.033	.497**	−.171	−.107	.063	.512**	1
	sig. (2-tailed)	.055	.580	.070	.009	.860	.004	.350	.559	.733	.003
	N	32	32	32	32	32	32	32	32	32	32	32

Table 2.

Correlations Matrix of water samples in Poopó Basin, Bolivian Altiplano.

*

. Correlation is significant at the 0.05 level (2-tailed).

**

. Correlation is significant at the 0.01 level (2-tailed).

The results of the KMO and Bartlett's sphericity are (Table 3):

KMO and Bartlett’s Test
Kaiser Meyer Olkin Measure of Sampling Adequacy		.478
Bartlett’s Test of Sphericity	Approx. Chi-Square	349.409
	df	55
	Sig.	.000

Table 3.

KMO and Bartlett's sphericity results for water samples.

The KMO statistics has a value of 0.478 which indicates that the data is not suitable for PCA, although Bartlett's test of sphericity has a Sig of 0.000. This means that the data is not suitable for a PCA.

Table 4 correspond to an analysis of metals in soils samples carried out in the Bolivian altiplano, Poopó Basin, Bolivia [2]. There are 36 sampling points in which 16 parameters have been determined. Therefore, we have a system with 33 elements and 16 variables.

No	Code	Al	As	B	Cd	Cr	Cu	Fe	Mn	Mo	Ni	P	Pb	S	Si	Sr	Zn
		mg/kg	mg/kg	mg/kg	mg/kg	mg/kg	mg/kg	mg/kg	mg/kg	mg/kg	mg/kg	mg/kg	mg/kg	mg/kg	mg/kg	mg/kg	mg/kg
1	COR 1H	13181.1	13.8	11.3	0.5	12.9	20.6	16708.9	233.7	0.2	8.0	532.5	35.6	556.9	429.9	42.5	86.8
2	COR 1C	11823.0	17.8	4.5	0.5	15.2	21.1	23063.1	474.0	0.3	10.1	337.6	40.9	300.5	519.2	32.5	84.2
3	COR 1P	12705.8	15.0	6.3	0.3	14.8	18.1	20914.0	370.3	0.3	9.5	345.5	35.1	161.0	459.4	26.3	85.2
4	COR 1AA	30996.3	38.5	15.0	0.9	40.2	48.6	57156.4	1029.9	0.8	27.4	976.4	88.3	581.1	1183.3	55.5	232.5
5	COR 2C	7945.6	28.0	8.9	0.7	10.2	20.1	15650.0	262.1	0.3	4.4	298.4	61.3	241.5	509.1	30.1	77.8
6	COR 2P	11231.6	31.2	6.9	0.7	10.9	21.3	16403.3	299.2	0.5	7.5	285.8	104.4	424.9	98.4	31.4	76.3
7	COR 2AA	8736.8	26.1	12.1	0.5	10.0	20.9	15818.3	332.4	0.3	5.8	407.7	48.7	373.7	449.3	37.8	99.5
8	COR 3H	10296.9	27.8	13.1	0.6	10.5	17.6	16405.1	394.2	0.5	6.8	457.7	40.3	348.8	535.2	33.3	81.4
9	COR 3C	4372.9	16.2	4.7	0.2	5.9	8.7	10264.0	192.5	0.3	3.4	218.9	20.4	168.4	375.9	15.6	54.5
10	COR 3P	6899.8	20.8	5.4	0.4	8.9	12.8	14938.4	281.6	0.3	5.1	279.2	30.6	153.6	455.2	21.8	67.0
11	COR 3AA	6910.1	21.5	6.7	0.5	9.1	16.0	15030.0	303.4	0.2	5.1	274.4	37.2	181.8	504.6	22.7	77.8
12	VM 1H	42276.0	30.1	40.0	1.2	27.1	27.8	22425.4	546.1	2.8	7.7	910.0	85.9	506.3	983.3	51.2	159.4
13	VM 1C	25081.6	23.0	27.5	0.3	17.4	11.5	16043.0	365.0	0.4	4.7	381.1	26.0	264.1	985.4	44.1	58.0
14	VM 2H	43636.7	17.3	29.5	0.3	29.2	18.8	22690.3	448.1	0.3	10.3	469.2	28.0	227.9	1138.1	39.1	78.0
15	VM 2P	40756.0	19.3	27.5	0.3	28.2	18.7	22097.1	428.5	0.4	8.8	449.3	25.6	220.4	1042.0	39.3	72.3
16	VM 3H	5509.4	9.3	8.3	0.4	5.2	9.4	8763.7	144.1	0.5	3.7	198.2	15.8	170.1	558.5	18.5	95.6
17	VM 3C	11299.4	13.3	3.8	0.6	15.3	22.9	23362.0	454.6	0.5	10.8	352.7	35.4	162.2	460.5	27.1	81.4
18	VM 3P	12348.8	15.9	4.8	0.4	16.3	25.5	25623.8	497.5	0.3	11.5	393.5	41.5	180.9	458.4	28.9	91.7
19	VM 4H	12362.6	19.7	20.5	0.8	11.1	21.8	17023.4	292.1	0.6	8.0	533.1	39.5	424.4	1395.9	51.3	203.0
20	VM 4C	25008.0	40.2	14.5	0.7	30.6	41.1	46040.2	928.5	0.9	18.9	813.9	70.8	398.4	1109.0	63.3	146.4
21	VM 4P	8614.9	18.5	23.3	0.8	9.1	16.6	18128.2	627.7	0.4	7.5	457.9	32.4	584.8	617.7	35.2	179.4
22	VM 5H	6887.9	28.9	11.8	0.9	10.0	22.1	238.7	503.4	0.3	7.8	362.5	70.2	844.3	487.6	25.5	130.2
23	VM 5C	7839.3	28.4	13.3	0.9	10.8	22.5	21060.7	505.6	0.3	7.3	371.0	73.0	818.4	488.2	26.0	137.5
24	VM 6C	7941.5	19.0	9.3	0.4	8.9	14.8	16193.1	510.6	0.3	6.5	328.9	43.9	360.1	575.9	24.6	88.5
25	VM 6P	6511.7	27.2	8.6	1.1	9.3	21.1	21475.7	544.7	0.2	6.7	364.7	53.6	414.0	506.9	19.5	161.2
26	POO 1C	10751.3	19.8	5.7	0.9	12.3	20.3	19361.9	424.3	0.5	8.6	348.3	43.4	191.3	633.8	27.3	90.8
27	POO 1P	13660.9	20.6	7.1	0.5	14.4	21.0	22414.2	485.6	0.6	9.4	348.3	33.7	181.2	606.7	33.8	76.1
28	POO 2C	10290.1	15.7	13.5	1.0	10.3	14.0	14995.4	340.5	0.4	5.2	337.6	27.9	179.9	516.9	36.1	117.9
29	POO 2P	10725.5	19.3	6.7	0.4	12.2	15.7	17443.0	386.6	0.2	6.8	295.3	30.9	214.1	552.8	29.0	68.3
30	POO 3C	7681.3	27.0	8.4	2.1	9.9	19.1	17784.7	297.0	0.3	6.4	688.2	138.7	300.1	496.8	30.3	246.6
31	POO 3P	9274.6	21.2	12.1	1.5	11.0	20.8	17636.1	337.4	0.4	6.0	803.9	95.2	289.3	517.9	36.9	193.8
32	POO 4C	7099.8	14.3	9.9	0.3	10.9	12.2	14469.9	286.8	0.7	7.5	250.7	24.8	171.4	440.3	26.0	51.7
33	POO 4C (Alta)	9838.7	17.5	11.7	0.4	10.3	13.0	14625.4	277.9	0.3	5.1	331.2	24.4	182.9	503.2	46.3	47.7
34	POO 4P	10407.3	16.3	11.7	0.6	11.3	15.1	16412.7	359.6	0.3	6.5	348.0	38.3	292.0	664.4	33.9	69.1
35	POO 4 AA	25849.4	14.6	28.9	0.3	18.6	12.7	14794.3	311.3	0.3	5.6	315.7	27.1	583.4	1439.7	54.3	57.0
36	PUÑ 4P	22049.2	16.5	21.2	0.2	15.2	9.3	12327.1	348.1	0.5	4.8	317.3	16.6	232.0	1308.1	43.7	45.5
37	Referencia	33277.5	18.4	23.7	3.9	74.5	356.4	26390.7	491.4	0.4	300.2	969.5	101.5	1841.5	501.3	81.0	744.7

Table 4.

Metals and trace elements analysis in soils from Poopó Basin, in Bolivian Altiplano [3].

Table 5 shows the correlation matrix, where it can be seen that there are correlations between the different variables. KMO’s and Bartlett’s tests give the following results: The KMO statistics is 0.704 and indicates that the data is acceptable (Table 6) for performing a PCA. The Sig. of the Bartlett test is 0.000 and indicates that the alternative hypothesis is valid, thus, the correlation matrix is not an identity. Then, these values indicate that the data can be subjected to a PCA. Therefore, we proceed with the PCA.

Correlations
		Al	As	B	Cd	Cr	Cu	Fe	Mn	Mo	Ni	P	Pb	S	Si	Sr	Zn
Al	Pearson Correlation	1	,207	,796**	−,115	,876**	,353*	,452**	,400*	,512**	,412*	,505**	,012	,092	,716**	,651**	,039
	Sig. (2-tailed)		,227	,000	,504	,000	,035	,006	,016	,001	,012	,002	,946	,595	,000	,800	,819
	N	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36
As	Pearson Correlation	,207	1	,124	,449**	,421*	,726**	,528**	,635**	,334*	,508**	,595**	,700**	,481**	,106	,354*	,503**
	Sig. (2-tailed)	,227		,472	,006	,011	,000	,001	,000	,047	,002	,000	,000	,003	,539	,034	,002
	N	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36
B	Pearson Correlation	,796**	,124	1	,003	,528**	,056	,083	,184	,530**	,028	,414*	−,034	,327	,732**	,642**	,136
	Sig. (2-tailed)	,000	.472		,988	,001	,745	,632	,282	,001	,871	,012	,845	,052	,000	,000	,429
	N	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36
Cd	Pearson Correlation	−,115	,449**	,003	1	−,030	,355*	,133	,189	,238	,099	,581**	,823**	,310	−,118	,057	,826**
	Sig. (2-tailed)	,504	,006	,988		,864	,033	,438	,271	,163	,567	,000	,000	,066	,491	,743	,000
	N	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36
Cr	Pearson Correlation	,876**	,421*	,528**	−,030	1	,700**	,788**	,705**	,443**	,786**	,660**	,167	,154	,638**	,685**	,218
	Sig. (2-tailed)	,000	,011	,001	,864		,000	,000	,000	,007	,000	,000	,331	,368	,000	,000	,202
	N	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36
Cu	Pearson Correlation	,353*	,726**	,056	,355*	,700**	1	,856**	,834**	,366*	,898**	,760**	,553**	,396*	,225	,492**	,587**
	Sig. (2-tailed)	,035	,000	,745	,033	,000		,000	,000	,028	,000	,000	,000	,017	,187	,002	,000
	N	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36
Fe	Pearson Correlation	,452**	,528**	,083	,133	,788**	,856**	1	,825**	,272	,915**	,665**	,298	,091	,348*	,521**	,414*
	Sig. (2-tailed)	,006	,001	,632	,438	,000	,000		,000	,109	,000	,000	,077	,596	,037	,001	,012
	N	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36
Mn	Pearson Correlation	,400*	,635**	,184	,189	,705**	,834**	,825**	1	,310	,857**	,622**	,309	,401*	,336*	,442**	,470**
	Sig. (2-tailed)	,016	,000	,282	,271	,000	,000	,000		,065	,000	,000	,067	,015	,045	,007	,004
	N	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36
Mo	Pearson Correlation	,512**	,334*	,530**	,238	,443**	,366*	,272	,310	1	,224	,564**	,271	,152	,296	,413*	,257
	Sig. (2-tailed)	,001	,047	,001	,163	,007	,028	,109	,065		,190	,000	,110	,376	,079	,012	,130
	N	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36
Ni	Pearson Correlation	,412*	,508**	,028	,099	,786**	,898**	,915**	,857**	,224	1	,629**	,299	,238	,321	,476**	,421*
	Sig. (2-tailed)	,012	,002	,871	,567	,000	,000	,000	,000	,190		,000	,077	,163	,056	,003	,010
	N	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36
P	Pearson Correlation	,505**	,595**	,414*	,581**	,660**	,760**	,665**	,622**	,564**	,629**	1	,622**	,352*	,395*	,648**	,744**
	Sig. (2-tailed)	,002	,000	,012	,000	,000	,000	,000	,000	,000	,000		,000	,035	,017	,000	,000
	N	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36
Pb	Pearson Correlation	,012	,700**	−,034	,823**	,167	,553**	,298	,309	,271	,299	,622**	1	,414*	−,147	,137	,701**
	Sig. (2-tailed)	,946	,000	,845	,000	,331	,000	,077	,067	,110	,077	,000		,012	,392	,425	,000
	N	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36
S	Pearson Correlation	,092	,481**	,327	,310	,154	,396*	,091	,401*	,152	,238	,352*	,414*	1	,168	,284	,453**
	Sig. (2-tailed)	,595	,003	,052	,066	,368	,017	,596	,015	,376	,163	,035	,012		,328	,093	,006
	N	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36
Si	Pearson Correlation	,716**	,106	,732**	−,118	,638**	,225	,348*	,336*	,296	,321	,395*	−.147	,168	1	,737**	,163
	Sig. (2-tailed)	,000	,539	,000	,491	,000	,187	,037	,045	,079	,056	,017	,392	,328		,000	,342
	N	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36
Sr	Pearson Correlation	,651**	,354*	,642**	,057	,685**	,492**	,521**	,442**	,413*	,476**	,648**	,137	,284	,737**	1	,253
	Sig. (2-tailed)	,000	,034	,000	,743	,000	,002	,001	,007	,012	,003	,000	,425	,093	,000		,136
	N	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36
Zn	Pearson Correlation	,039	,503**	,136	,826**	,218	,587**	,414*	,470**	,257	,421*	,744**	,70l**	,453**	,163	,253	1
	Sig. (2-tailed)	,819	,002	,429	,000	,202	,000	,012	,004	,130	,010	,000	,000	,006	,342	,136
	N	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36	36

Table 5.

Sample correlation matrix of metal and trace elements in soil samples.

**

Correlation is significant at the 0.01 level (2-tailed).

*

Correlation is significant at the 0.05 level (2-tailed).

KMO and Bartlett’s Test
Kaiser Meyer Olkin Measure of Sampling Adequacy		.704
Bartlett’s Test of Sphericity	Approx. Chi-Square	725.706
	df	120
	Sig.	.000

Table 6.

KMO and Bartlett’s sphericity results for soil samples.

Four main components have been extracted. The principal extracted components are presented in Table 7. The table shows that with four components, 85.13% of the variability would be explained.

Total variance explained
Component	Initial eigenvalues			Extraction sums of squared loadings			Rotation sums of squared loadings
	Total	% of variance	Cumulative %	Total	% of variance	Cumulative %	Total	% of variance	Cumulative %
1	7.584	47.401	47.401	7.584	47.401	47.401	4 732	29.578	29.578
2	3.192	19.948	67.350	3.192	19.948	67.350	4.070	25.435	55.013
3	1.905	11.904	79.254	1.905	11.904	79.254	3.639	22.743	77.756
4	.941	5.880	85.134	.941	5.880	85.134	1.181	7.379	85.134
5	.735	4.596	89.731
6	.466	2.913	92.643
7	.381	2.381	95.024
8	.289	1.805	96.829
9	.164	1.025	97.854
10	.110	.690	98.544
11	.074	.462	99.006
12	.065	.405	99.411
13	.049	.304	99.715
14	.029	.181	99.896
15	.011	.072	99.968
16	.005	.032	100.000

Table 7.

Extraction of principal components (PC) with a total explained variance of 85.13%.

Extraction Method: Principal Component Analysis

Table 8 shows the rotated component matrix with the Varimax rotation method. According to this matrix, the representativeness of the main components with respect to the variables is determined. The highest correlation that the variable has with the main component was taken as a criterion.

Rotated component matrix^a
	Component
	1	2	3	4
Al	.320	.874	−.056	−.101
As	.523	.083	.547	.314
B	−.116	.945	.057	.197
Cd	−.011	−.068	.946	.056
Cr	.719	.647	.016	−.065
Cu	.861	.132	.412	.125
Fe	.928	.203	.155	−.104
Mn	.850	.199	.191	.233
Mo	.099	.609	.432	−.250
Ni	.956	.142	.115	.046
P	.500	.470	.658	.001
Pb	.220	−.078	.885	.129
S	.119	.161	.328	.874
Si	.210	.825	−.145	.166
Sr	.376	.746	.093	.163
Zn	.280	.073	.809	.214

Table 8.

Rotated component matrix.

Extraction Method: Principal Component Analysis.

Rotation Method: Varimax with Kaiser Normalization.

^aRotation converged in 5 iterations.

$$\mathit{PC}1=\mathit{Ni}+\mathit{Fe}+\mathit{Cu}+\mathit{Mn}+\mathit{Cr}$$

$$\mathit{PC}2=B+\mathit{Al}+\mathit{Si}+\mathit{Sr}+\mathit{Mo}$$E1

$$\mathit{PC}3=\mathit{Cd}+\mathit{Pb}+\mathit{Zn}+P+\mathit{As}$$

$$\mathit{PC}4=\mathit{Ni}+\mathit{Fe}+\mathit{Cu}+\mathit{Mn}+\mathit{Cr}$$

Table 9 shows the Component Score Coefficients Matrix, which are the coefficients of the variables in each PCA. For example, for Principal Component 1 (PC1), the following Eq. (2) applies:

Matriz de coeficiente de puntuación de componente
	Componente
	1	2	3	4
Al	−,007	,236	−,027	−,140
As	,078	−,050	,079	,192
B	−,184	,308	,020	,145
Cd	−,125	−,003	,351	−,124
Cr	,145	,108	−,066	−,117
Cu	,206	−,076	,018	,017
Fe	,259	−,058	−,043	−,168
Mn	,220	−,063	−,084	,166
Mo	−,106	,200	,213	−,365
Ni	,278	−,089	−,093	−,008
P	,009	,093	,193	−,161
Pb	−,041	−,043	,282	−,044
S	−,051	,000	−,057	,803
Si	−,031	,222	−,099	,150
Sr	,002	,178	−,032	,101
Zn	−,034	−,009	,231	,048

Table 9.

Component score coefficients matrix.

Método de extracción: análisis de componentes principales.

Método de rotación: Varimax con normalización Kaiser.

Puntuaciones de componente.

$$\begin{array}{ll}\mathit{PC}1=& -0.007\ast \mathit{Al}+0.078\ast \mathit{As}-0.184\ast B-0.125\ast \mathit{Cd}+0.145\ast \mathit{Cr}+0.206\ast \mathit{Cu}\\ & +0.259\ast \mathit{Fe}+0.220\ast \mathit{Mn}-0.106\ast \mathit{Mo}+0.278\ast \mathit{Ni}+0.009\ast P-0.041\ast \mathit{Pb}\\ & -0.051\ast S-0.031\ast \mathit{Si}+0.002\ast \mathit{Sr}-0.034\ast \mathit{Zn}\end{array}$$E2

Similarly, the equations for the components PC2, PC3 and PC4 can be expressed.

According to this matrix of score coefficients and their corresponding equations, the score values of the main components are obtained for the 36 sampling points. These are shown in Table 10.

Sample	${\mathrm{CP}}_1$	${\mathrm{CP}}_2$	${\mathrm{CP}}_3$	${\mathrm{CP}}_4$
1	−0.21118	−0.0777	−0.33467	0.80961
2	0.6651	−0.67391	−0.53521	−0.20777
3	0.39744	−0.60917	−0.64339	−0.954
4	4.07162	0.56719	0.76641	0.55046
5	−0.34113	−0.59646	0.24423	−0.13876
6	−0.07872	−0.94299	0.7625	0.27764
7	−0.18808	−0.3646	0.02199	0.54976
8	−0.16801	−0.19284	0.04181	0.26754
9	−0.79917	−0.90177	−0.74427	−0.65343
10	−0.33788	−0.78329	−0.45122	−0.68191
11	−0.27713	−0.79168	−0.32166	−0.4073
12	−0.67221	3.28014	2.51067	−1.29964
13	−0.61199	1.3241	−0.81815	0.22432
14	0.33766	1.77831	−1.07201	−0.46932
15	0.23938	1.63463	−0.98365	−0.54454
16	−1.18136	−0.4418	−0.4608	−0.8548
17	0.68138	−0.72139	−0.37866	−1.24838
18	1.03018	−0.79119	−0.53675	−0.89173
19	−0.59117	1.09146	0.47815	0.82755
20	2.92182	0.70194	0.35112	0.21752
21	−0.32097	0.11616	0.21485	1.62766
22	−0.52482	−0.6866	0.55143	2.96642
23	0.00703	−0.71324	0.53004	2.46939
24	−0.07964	−0.61843	−0.43321	0.45935
25	0.13395	−1.0284	0.67803	0.67771
26	0.16106	−0.54494	0.12387	−0.82888
27	0.54161	−0.31881	−0.42751	−0.80632
28	−0.6818	−0.06185	0.23561	−0.69627
29	0.06159	−0.56759	−0.68723	−0.29851
30	−0.80934	−0.64774	3.33121	−0.66866
31	−0.59454	−0.14172	2.187	−0.70855
32	−0.38801	−0.34591	−0.64539	−0.98714
33	−0.47597	0.01196	−0.67739	−0.40583
34	−0.32046	−0.14616	−0.38936	−0.05153
35	−0.83523	1.86013	−1.28317	1.80646
36	−0.76102	1.34416	−1.20524	0.07187

Table 10.

Sampling point scores for principal components.

After these scores, which represent the new composite reduced variables, different graphical representations and interpretations can be made. For example, the plotting of each principal component with respect to the sampling points (Figure 1).

Figure 1.

Representation of the main components PC1 and PC2 with respect to the sampling points.

Figure 1a shows that in the sampling points there is a certain homogeneous distribution of PC1 with respect to the points, except for points 4 (Code sample, CORR 1AA) and 20 (Code sample, VM 4C). This indicates that there are high outliers in PC1 (Ni, Fe, Cu, Mn and Cr). In environmental terms, special attention is required at these sampling points. The points in question are (Table 11):

No	Code Soil	Cr mg/kg	Cu mg/kg	Fe mg/kg	Mn mg/Kg	Ni mg/kg
4	COR 1AA	40.2	48.6	5756.4	1029.9	27.4
20	VM 4C	30.6	41.1	46040.2	928.5	18.9
	Max	40.2	48.6	57156.4	1029.9	27.4
	Min	5.2	8.7	238.7	144.1	3.4
	Mean	14.3	19.3	19049.5	411.18	7.9

Table 11.

Inhomogeneous distribution in soil samples.

The samples have high values in these metals. Particularly, sample number 4 presents the maximum values and, sample number 20 is well above the average values. Similar analysis can be done for the other principal components.

Regarding structure, the samples numbers 4 and 20 form a group with relatively high values of PC1. Another group is formed by the rest of the points. Figure 1b represents the distribution of PC2 (B, Al, Si, Sr and Mo). It can also be seen that there are atypical points forming a group with relatively high values in this component. These are sampling points 12, 14, 15, 35 and 36. The rest of the points form a group with a homogeneous distribution in relation to PC2.

Figure 2a shows that the behavior of the PC3 is also homogeneous, with the exception of sampling points 12, 30, and 31 that would have high outliers in Cd, Pb, Zn, P and As. Regarding structure, sampling points 12, 30 and 31 form a group with high values of PC3, and the other group formed by the rest of the sampling points. Figure 2b represents the distribution of sulfur in the sampling points. It can be seen that one group would be made up of sampling points 21, 22, 23 and 35 with relatively high sulfur values, and the other group made up of the rest of the points.

Figure 2.

Representation of the main components PC3 and PC4 with respect to the sampling points.

Figure 3 is the representation of PC1 against PC2. There are three groups observed; the first group formed by sampling points 12, 13, 14, 15, 19, 35 and 36, with high values of PC2 (B, Al, Si, Sr and Mo) with respect to their values of PC1 (Ni, Fe, Cu, Mn and Cr); a second group made up of sampling points 4 and 20 which would have high values of PC1 in relation to PC2; and a third group made up of the rest of the sampling points which would have an homogeneous distribution in PC2 and PC1. Again, from the environmental point of view, the sampling points of the first and second groups should be analyzed more carefully.

Figure 3.

Representation of the main components PC2 against PC1.

Figure 4 shows the distribution of the samples in relation to the main components PC1 against PC3. While the PC3 in most of the sampling points does not show variability except for points 12, 30 and 31; PC1 is highly distributed with the greatest variability in the sampling points.

Figure 4.

Representation of the main components PC3 against PC1.

In the same way, graphical representations of the rest of the combinations of the main components can be made (Figures 5 and 6).

Figure 5.

Representation of the main components PC4 against PC1.

Figure 6.

Representation of the main components PC3 against PC2.

In the following example, two types of soils have been considered. The characteristics of both are different, and this fact will allow us to see the ability of the main components to characterize and classify soils [4].

The following chemical parameters have been considered: pH in H₂O, pH in KCl solution, Electrical Conductivity (EC), Change acidity, Total Nitrogen, Organic Matter, Assimilable Phosphorus and Exchangeable Cations (Ca²⁺, Mg²⁺, Na⁺, K⁺).

The first group of samples comes from the inter-Andean valley of the Municipality of Inquisivi – Yamora, which is located between the coordinates: 66^o43′29″ and 67^o17′58″ West longitude; 15^o47′34″ and 17^o18′20″ South latitude and at an average altitude of 2840 m (a.s.l.). The second sample comes from the Northern Altiplano Viacha Municipality, located between the coordinates: 68^o16′56″ and 68^o22′72″ West longitude and 16^o32′39″ and 16^o54′44″ latitude, with an average altitude of 4070 m (a.s.l.), both in La Paz, Bolivia [4].

The ten soil samples have been taken in the Yamora community, and another 10 soil samples from the Viacha community. The mentioned 11 parameters have been analyzed. The evaluation does not take into account the environmental conditions of Yamora or Viacha. It is only carried out based on the chemical parameters for the evaluation of fertility from the chemical point of view of the soils (Table 12).

Location	pH (H2O)	pH (KCl)	CE	H-Al	% MO	% N	Na	K	Ca	Mg	P
Yamora	6.75	5.8	0.075	0.0329	3.4	0.28	0.128	0.688	17.761	2.548	273.916
Yamora	6.76	4.98	0.075	0.0609	3.2	0.30	0.128	0.688	17.760	2.577	255.876
Yamora	6.72	5.73	0.068	0.0339	3.3	0.31	0.134	0.688	18.331	2.636	250.994
Yamora	6.76	5.89	0.074	0.0082	3.4	0.32	0.134	0.655	18.674	2.684	257.253
Yamora	6.73	5.89	0.072	0.0329	3.2	0.30	0.134	0.655	17.455	2.518	246.810
Yamora	6.79	5.92	0.068	0.0329	3.4	0.32	0.146	0.655	17.799	2.548	266.998
Yamora	6.79	5.37	0.069	0.0391	3.4	0.3	0.128	0.688	17.874	2.587	253.086
Yamora	6.8	5.84	0.073	0.0329	3.4	0.3	0.134	0.655	17.074	2.450	259.345
Yamora	6.83	6.01	0.072	0.0349	3.4	0.3	0.134	0.655	18.027	2.606	261.420
Yamora	6.82	5.95	0.072	0.0329	3.1	0.3	0.134	0.622	17.341	2.479	275.347
Viacha	8.54	7.13	0.727	0.0934	0.7	0.086	4.663	0.459	5.385	4.008	16.010
Viacha	8.72	7.16	0.732	0.0934	0.7	0.096	5.012	0.491	5 155	4.066	15.870
Viacha	8.78	7.12	0.736	0.1054	0.7	0.101	4.605	0.426	5.042	3.988	18.241
Viacha	8.74	7.11	0.735	0.1054	0.5	0.093	4.605	0.426	5.080	3.988	19.287
Viacha	8.81	7.16	0.737	0.0934	0.6	0.092	4.663	0.426	5.118	4.027	19.845
Viacha	8.78	7.12	0.738	0.1054	0.7	0.091	4.663	0.459	5.118	4.027	20.612
Viacha	8.94	7.01	0.731	0.1091	0.7	0.093	4.605	0.426	5.080	3.959	17.683
Viacha	8.69	6.78	0.733	0.0813	0.6	0.093	4.663	0.426	5.309	3.802	18.241
Viacha	8.49	7.14	0.732	0.0818	0.7	0.093	5.129	0.491	5.233	3.978	18.311
Viacha	8.81	7.14	0.780	0.0813	0.5	0.093	5.246	0.491	4.889	3.939	16.010

Table 12.

Results of the analysis of parameters in samples from Yamora and Viacha.

Reproduced with permission from Revista Boliviana de Química; Excerpt from [4].

PCA was also performed and the correlation matrix is shown in Table 13.

Correlaciones
		pHenH2O	pHenKCl	CE	H_Al	MO	N	Na	K	Ca	Mg	P
pHenH2O	Correlación de Pearson	1	.944**	.996**	.945**	−.994**	−.992**	.991**	−.978**	−.996**	.991**	−.993**
	Sig. (bilateral)		.000	.000	.000	.000	.000	.000	.000	.000	.000	.000
	N	20	20	20	20	20	20	20	20	20	20	20
pHenKCl	Correlación de Pearson	.944**	1	.947**	.836**	−.941**	−.941**	.948**	−.940**	−.947**	.947**	−.941**
	Sig. (bilateral)	.000		.000	.000	.000	.000	.000	.000	.000	.000	.000
	N	20	20	20	20	20	20	20	20	20	20	20
CE	Correlación de Pearson	.996**	.947**	1	.936**	−.998**	−.997**	.998**	−.971**	−.999**	.995**	−.998**
	Sig. (bilateral)	.000	.000		.000	.000	.000	.000	.000	.000	.000	.000
	N	20	20	20	20	20	20	20	20	20	20	20
H_Al	Correlación de Pearson	.945**	.836**	.936**	1	−.939**	−.942**	.925**	−.921**	−.943**	.936**	−.938**
	Sig. (bilateral)	.000	.000	.000		.000	.000	.000	.000	.000	.000	.000
	N	20	20	20	20	20	20	20	20	20	20	20
MO	Correlación de Pearson	−.994**	−.941**	−.998**	−.939**	1	.995**	−.996**	.975**	.997**	−.991**	.996**
	Sig. (bilateral)	.000	.000	.000	.000		.000	.000	.000	.000	.000	.000
	N	20	20	20	20	20	20	20	20	20	20	20
N	Correlación de Pearson	−.992**	−.941**	−.997**	−.942**	.995**	1	−.994**	.967**	.997**	−.990**	.994**
	Sig. (bilateral)	.000	.000	.000	.000	.000		.000	.000	.000	.000	.000
	N	20	20	20	20	20	20	20	20	20	20	20
Na	Correlación de Pearson	.991**	.948**	.998**	.925**	−.996**	−.994**	1	−.960**	−.996**	.993**	−.996**
	Sig. (bilateral)	.000	.000	.000	.000	.000	.000		.000	.000	.000	.000
	N	20	20	20	20	20	20	20	20	20	20	20
K	Correlación de Pearson	−.978**	−.940**	−.97l**	−.921**	.975**	.967**	−.960**	1	.974**	−.962**	.969**
	Sig. (bilateral)	.000	.000	.000	.000	.000	.000	.000		.000	.000	.000
	N	20	20	20	20	20	20	20	20	20	20	20
Ca	Correlación de Pearson	−.996**	−.947**	−.999**	−.943**	.997**	.997**	−.996**	.974**	1	−.991**	.997**
	Sig. (bilateral)	.000	.000	.000	.000	.000	.000	.000	.000		.000	.000
	N	20	20	20	20	20	20	20	20	20	20	20
Mg	Correlación de Pearson	.991**	.947**	.995**	.936**	−.991**	−.990**	.993**	−.962**	−.991**	1	−.995**
	Sig. (bilateral)	.000	.000	.000	.000	.000	.000	.000	.000	.000		.000
	N	20	20	20	20	20	20	20	20	20	20	20
P	Correlación de Pearson	−.993**	−.941**	−.998**	−.938**	.996**	.994**	−.996**	.969**	.997**	−.995**	1
	Sig. (bilateral)	.000	.000	.000	.000	.000	.000	.000	.000	.000	.000
	IM	20	20	20	20	20	20	20	20	20	20	20

Table 13.

Matrix of correlations of samples from Yamora and Viacha.

**

. La correlación es significativa en el nivel 0,01 (2 colas).

In the correlation matrix, high correlations between the variables are observed, the KMO with 0.865 and a Bartlett Significance of 0.000 indicate that the reduction of dimensions by principal components is feasible and adequate (Table 14). Therefore, we proceeded to obtain two main components (Table 15) and the rotated component matrices and component score coefficients for the samples (Table 16) with the application of Varimax rotation and Kaiser normalization.

KMO and Bartlett’s Test
Kaiser Meyer Olkin Measure of Sampling Adequacy		.865
Bartlett’s Test of Sphericity	Approx. Chi-Square	715.671
	df	55
	Sig.	.000

Table 14.

KMO and Bartlett's sphericity results for soils samples.

Total variance explained
Component	Initial eigenvalues			Extraction sums of squared loadings			Rotation sums of squared loadings
	Total	% of variance	Cumulative %	Total	% of variance	Cumulative %	Total	% of variance	Cumulative %
1	10.707	97.338	97.338	10.707	97.338	97.338	5.673	51.572	51.572
2	.166	1.511	98.848	.166	1.511	98.848	5.200	47.276	98.848
3	.063	.569	99.417
4	.038	.342	99.759
5	.011	.103	99.862
6	.006	.056	99.918
7	.004	.041	99.959
8	.003	.024	99.983
9	.001	.012	99.995
10	.000	.003	99.998
11	.000	.002	100.000

Table 15.

Extraction of principal components with a total explained variance of 98.84%.

Extraction Method: Principal Component Analysis.

Rotated component matrix^a
	Component
	1	2
pHenH2O	.711	.699
pHenKCl	.876	.461
CE	.728	.683
H_Al	.476	.870
MO	−.717	−.694
N	−.710	−.699
Na	.739	.667
K	−.725	−.657
Ca	−.718	−.694
Mg	.723	.682
P	−.717	−.693

Component score coefficient matrix
	Component
	1	2
pHenH2O	.011	.123
pHenKCl	1.195	−1.122
CE	.106	.024
H_Al	−1.184	1.367
MO	−.041	−.092
N	−.007	−.128
Na	.185	−.059
K	−.174	.049
Ca	−.047	−.086
Mg	.095	.035
p	−.045	−.087

Table 16.

Rotated component matrix and component score coefficient matrix for the Yamora and Viacha samples.

Extraction Method: Principal Component Analysis.

Rotation Method: Varimax with Kaiser Normalization.

Component Scores.

^aRotation converged in 3 iterations.

The rotated component matrix shows that there is a structure. A group of parameters that have a positive correlation with the principal components, Group 1 (PC1): pH in KCl, Na⁺, CE, Mg²⁺, pH in H2O and H-Al with positive correlation. There is another group of parameters that have a negative correlation, Group 2 (PC2): N, MO, P, Ca²⁺ and K⁺. This leads to a competition between these groups of parameters in the soil. If Group 1 overlaps Group 2, the soil would have high pH and EC values, high Na⁺ and Mg²⁺ contents, and positive values of the main components, poor exchange content of OM, P and N. It means that there is an unfavorable soil for agriculture purposes. However, if Group 2 of parameters overlaps Group 1, then the soil is rich in OM, P and N. This means that the soil is more suitable for agriculture purposes, and it would have negative values of the main components.

The score coefficient matrix of the components generates the functions of PC1 and PC2:

$$\begin{array}{l}\mathit{PC}1=0.011\ast \mathit{pH}\left(H2O\right)+1.195\ast \mathit{pH}\left(\mathit{KCl}\right)+0.106\ast \mathit{CE}-1.184\ast H_{\mathit{Al}}\\ -0.041\ast \mathit{OM}-0.007\ast N+0.185\ast \mathit{Na}-0.174\ast K-0.047\ast \mathit{Ca}+0.095\ast \mathit{Mg}\\ -0.045\ast P\end{array}$$E3

$$\begin{array}{l}\mathit{PC}1=0.123\ast \mathit{pH}\left(H2O\right)-1.122\ast \mathit{pH}\left(\mathit{KCl}\right)+0.024\ast \mathit{CE}+1.367\ast H_{\mathit{Al}}\\ -0.092\ast \mathit{OM}-0.128\ast N-0.059\ast \mathit{Na}-0.049\ast K-0.086\ast \mathit{Ca}+0.035\ast \mathit{Mg}\\ -0.087\ast P\end{array}$$E4

The score values are the following (Table 17):

Location	CP1	CP2
Yamora	−0.6039	−0.7968
Yamora	−2.9276	1.6177
Yamora	−0.7392	−0.6686
Yamora	0.4893	−2.0047
Yamora	−0.3933	−0.9410
Yamora	−0.3570	−1.0346
Yamora	−1.5191	0.1140
Yamora	−0.4907	−0.8760
Yamora	−0.2710	−1.0577
Yamora	−0.2547	−1.0504
Viacha	0.8095	0.5245
Viacha	0.8482	0.5004
Viacha	0.4159	1.0341
Viacha	0.4046	1.0660
Viacha	0.9214	0.4989
Viacha	0.3742	1.0584
Viacha	0.1010	1.3822
Viacha	0.6979	0.5567
Viacha	1.2224	0.0200
Viacha	1.2719	0.0567

Table 17.

Principal component coefficients for the Yamora and Viacha samples.

The representation of the components for the Yamora and Viacha samples are shown in Figure 7. For both PC1 (Figure 7a) and PC2 (Figure 7b), the positive values indicate that the pH parameters in KCl, Na⁺, EC, Mg²⁺, pH in H₂O, and H-Al overlap the parameters of N, OM, P, Ca²⁺, K⁺. This means that if the soils have positive values of PC1 and PC2, then the soil has high pH values, high Na⁺ concentration, and high EC. On the other hand, if the soil has negative values of the components, then the soil is rich in OM, P, N, which represents a much more suitable land for agriculture.

Figure 7.

Principal Component Analysis of the Yamora and Viacha samples a) Principal Component PC1, b) Principal Component PC2.

In the case of the Yamora samples, its PC1 and PC2 is negative, therefore, this soil is rich in OM, P and N, which represents a much more suitable soil for agriculture. In the results for the Viacha samples, the PC1 and PC2 are positive, therefore, this soil is shown as a soil not so suitable for agriculture (Figure 8).

Figure 8.

Principal components PC1 and PC2 from Yamora and Viacha samples.

It can be observed that the main components accurately classify the two types of soils. In addition, a correlation can be observed for each type of soil (Figure 9).

Figure 9.

The main components PC1 and PC2 show correlation for each type of soil, Yamora and Viacha.

The slope of both is approximately the same and the characterization of the soils is given by the ordinate to the origin (Figure 9). Soils with more suitable characteristics for cultivation, that is, the parameters N, OM, P, Ca²⁺, K⁺ overlap the pH in KCl, Na⁺, EC, Mg²⁺, pH in H₂O and H-Al tend towards smaller or even negative ordinates to the origin. In this case, the main components are capable of classifying and characterizing the soils with high precision. Thus, the multivariate analysis of soils constitutes an important tool for classifying soils.

It should be considered that the principal components give us a stand point in the data analysis. These must be complemented with other methods of multivariate analysis. In this case; for example, multivariate discriminant analysis can be applied [5].

The coefficients of the standardized canonical discriminant function indicate that the most appropriate parameters considered in the discriminant function are N, Na⁺, K⁺, Mg²⁺ and P. The parameters that are important to define soil fertility are: pH and OM. In addition, other factors that intervene in soil formation are the presence of minerals that contain exchange cations (Na⁺, K⁺, Mg²⁺ and Ca²⁺), decreases in soil acidification and, the decomposition process of minerals.

The general discriminant function obtained for the two types of soils is [6]:

$$D=-18.418+118.391\ast N-8.267\ast \mathit{Na}+67.852\ast K-11.752\ast \mathit{Mg}+0.114\ast P$$E5

While the discriminant functions by group are:

$$\begin{array}{ll}{D}_{\mathit{\text{Yamora}}}=& -4971.556+10936.736\ast N-553.970\ast \mathit{Na}+5449.136\ast K\\ & -206.719\ast \mathit{Mg}+13.873\ast P\end{array}$$E6

$$D_{\mathit{\text{Viacha}}}=-2725.256-3502.174N+454.280\mathit{Na}+2826.109K+1226.527\mathit{Mg}-0.023P$$E7

The results of the application of the discriminant function in the classification of the samples in both places indicate that the 20 samples can be classified 100% correctly. Therefore, the application of these functions in the classification of new soil samples has a high probability of classifying them correctly. In this way, it is possible to classify the soils through five parameters and the discriminant function, and thus, determine its chemical fertility. This information can be complemented to the main components.

3. Conclusions

The data analysis by main Principal Components Analysis for the reduction of dimensions in data was applied to soil samples. It is shown that this tool is fundamental and fully applicable, since it allows the characterization and classification of soil samples with precision. This brings a better interpretation of the results.

Acknowledgments

Due acknowledgement to Springer Nature for giving permission to reproduce Table 1 from “Sources and behavior of arsenic and trace elements in groundwater and surface water in the Poopó Lake basin, Bolivian Altiplano” by Oswaldo Eduardo Ramos Ramos, Luis Fernando Cáceres, Mauricio Rodolfo Ormachea Muñoz, Prosun Bhattacharya, Israel Quino, Jorge Quintanilla, Ondra Sracek, Roger Thunvik, Jochen Bundschuh, Maria Eugenia Garcia., Environmental Earth Sci., 66: 793 – 807, 2012.

A due acknowledgement to Revista Boliviana de Química for giving permission to reproduce the Table and the equation from “Chemometric evaluation of internal reference material (IRM) of agricultural soils in the two provincial municipalities of La Paz” by Rolando Mamani Quispe, Leonardo Guzmán Alegria, Jorge Chungara Castro, Oswaldo Eduardo Ramos Ramos, Revista Boliviana de Química, Vol. 39, No 4, pp 181 – 189, 2019; and “Análisis multivariable en la clasificación de suelos para la agricultura en el valle y Altiplano Boliviano” by Rolando Mamani Quispe, Oswaldo Eduardo Ramos Ramos, Jorge Chungara Castro, Leonardo Guzmán Alegría, Revista Boliviana de Química, Vol. 38, No 3, pp 126 – 132, 2021.

A due acknowledgment to José Antonio Bravo, Ph.D., Chief Editor of Revista Boliviana de Química for gramatical revision of the document.

Conflict of interest

The authors declare no conflict of interest.