J. Plant Nutr. Soil Sci. 2012, 000, 1 8 DOI: 10.1002/jpln.201100361 1
Analysis of soil fertility and its anomalies using an objective model
Francisco J. Moral1*, Francisco J. Rebollo2, and José M. Terrón3
1
Departamento de Expresión Gráfica, Escuela de Ingenierías Industriales, Universidad de Extremadura. Avda. de Elvas, s/n. 06071 Badajoz,
Spain.
2
Departamento de Expresión Gráfica, Escuela de Ingenierías Agrarias, Universidad de Extremadura. Carretera de Cáceres s/n,
06007 Badajoz, Spain.
3
Departamento de Cultivos Extensivos, Centro de Investigación La Orden-Valdesequera, Consejería de Empleo, Empresa e Innovación,
Junta de Extremadura. 06187 Guadajira, Badajoz, Spain.
Abstract
In this work, the use of an objective method, the formulation of the Rasch measurement model,
which synthesizes data with different units into a uniform analytical framework, is considered to
get representative measures of soil fertility potential in an experimental field. Thus, two types of
information about the soil were obtained from soil samples taken at 70 locations: first, the tex-
tural components were determined, and, secondly, deep (ECa-90) and shallow (ECa-30) soil
apparent electrical conductivity, approximately 0 90 and 0 30 cm depths, respectively, were
measured. A latent variable, denominated soil fertility potential, was defined. It is supposed, and
later it is verified, that all soil properties previously indicated have a marked influence on the
latent variable. The adequate assignment of categorical values across properties measures and
the good fit of the data are checked as a previous phase to properly compute the Rasch meas-
ures. After applying the Rasch methodology, it was obtained that both electrical conductivities
are the most influential properties on soil fertility potential, getting moreover a ranking of all soil
samples according to their fertility potential and the unexpected behaviors, called misfits, of
some soil samples, which constitute a very useful information to better match soil and crop
requirements as they vary in the field, being a rational basis for a site-specific crop manage-
ment.
Key words: Rasch model / texture / soil apparent electrical conductivity / site-specific soil management
Accepted January 8, 20152
1 Introduction
Obtaining a measure of soil fertility potential, in the sense the in agricultural soils and, in consequence, provide indications
crop-production potential is influenced by soil fertility, is not about their fertility (Moral et al., 2010).
easy due to the fact that different variables can influence its
quantification. Soil fertility is affected by many soil physical
and chemical variables, which, in turn, depend on various With the aim of considering and summarizing data from differ-
local factors, such as climatic conditions. ent variables, the Rasch model has been used successfully
in some environmental applications (e.g., Moral et al., 2006).
During the last years, the management of agricultural fields However, despite the useful information it can generate, this
tends to be differential, defining areas with similar character- technique had not been used in agronomic or soil research
istics, homogeneous zones, which will require different treat- until the work of Moral et al. (2011), in which different man-
ments. Variability management can improve the productivity agement zones were delimited in an experimental field taking
and profitability of crop production and also to protect envir- into account the formulation of the Rasch model with the aim
onmental resources. This can be accomplished by spatially of integrating soil textural and ECa data into an overall vari-
varying fertilizer according to crop requirement. Delineation able. Thus, an estimation of the soil fertility potential was ob-
of management zones can be done using some rather com- tained (the Rasch measure) and it was utilized as previous
plex techniques, and their results need a subsequent inter- information to carry out a geostatistical study and, later, by
pretation which is usually quite subjective (Morari et al., means of an equal-size classification method to delineate the
2009). homogeneous zones. However, as it was recognized in the
aforementioned work, besides providing soil-fertility-potential
Another problem is the correct choice of the variables that estimates, the output of the Rasch model contains a lot of
can better characterize soil fertility. In general, soil texture useful information as, for example, if all individual variables
properties and apparent electrical conductivity (ECa), the last support the latent variable, or if there is any anomaly related
integrating the response of several soil physical and chemical to a particular soil property. This information could be very
properties, have been utilized to characterize different zones important from an agronomic point of view.
* Correspondence: Dr. F. J. Moral; e-mail: [e-mail]
© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.plant-soil.com
2 Moral, Rebollo, Terrón J. Plant Nutr. Soil Sci. 2012, 000, 1 8
In this work we aim to: (1) analyze the proper use of the important to subjects (in this case soil samples) than other
Rasch model; (2) study the misfits since they could be an items. Thus, the Rasch model constructs a line of measure-
important source of information about anomalies in any soil ment with the items placed hierarchically on this line accord-
property or data at every sample location; and (3) incorporate ing to their importance to subjects. The validity of a given test
this information in a geographical information system (GIS) to can be assessed through examination of this item ordering,
visualize where anomalies are located and their possible spa- i.e., by assessing whether all items work together to measure
tial patterns. a single variable.
Rasch measurement construction applies a stochastic Gutt-
2 Materials and methods
man model to convert rating scale observations into linear
measures, to which linear statistics can be usefully applied,
2.1 The Rasch model and tests for goodness-of-fit to validate its item calibrations
and subject measures. In this case study, the Rasch model
The Rasch model is a simple but at the same time very
combines calibrations of soil-property items additively to soil-
powerful Item Response Theory model for measurement,
sample measures to define soil-fertility-potential probabilities.
being the most viable proposition for practical testing since it
This stochastic conjoint additivity specifies a Guttman scale
can be applied in the context in which individual, soil sam-
of probabilities to which the data are fitted (Rasch, 1980).
ples, interacts with items, soil properties (Ren et al., 2008).
In order to determine how well each item contributes to the
If guided by a reasonably coherent conceptual goal, the
soil-fertility-potential measurement, chi-square fit statistics,
Rasch model can synthesize and consolidate seemly dispa-
known as Infit and Outfit mean-square (Infit and Outfit
rate data into a uniform analytical framework. The purpose of
MNSQ), ratios of observed residual variance to expected
this procedure is to transcend several heterogeneous meas-
residual variance, should be computed. Infit is an informa-
ures of soil properties (clay, silt, sand, ECa-30, and ECa-90
tion-weighted or inlier-sensitive fit statistic that focuses on the
data [soil apparent electrical conductivity, approximately at
overall performance of an item or subject. Outfit is an outlier-
0 90 and 0 30 cm depths]) and consolidate them into an
sensitive fit statistic that picks up rare events that have
overall variable that simplifies interpretation of soil fertility
occurred in an unexpected way. Its expectation is 1. Values
potential.
> 2 indicate unexplained randomness throughout the data
(Smith, 1996). Usually, items that fall between the infit and
outfit limits of 0.6 and 1.5 are accepted and those with values
One way to form a single synthesis of the items, which are
beyond these thresholds have to be removed (Bond and Fox,
expressed in different measurement units, is by means of a
2007).
common referent that holds them all together. This referent,
which will be adimensional and constitute the latent variable
or construct, shall be termed  soil fertility potential . To More information about the mathematical formulation of the
Rasch model can be obtained in Moral et al. (2011).
achieve an adimensional characterization, we first categorize
the data corresponding to the considered individual soil prop-
erties. In particular, five categories or levels are established
2.2 Data collection and treatment
for all properties and these categories are the same for each
soil property. A measure assigned to level 0 indicates the low-
Soil samples were collected at a farm called Cerro del Amo
est contribution to soil fertility potential and, on the contrary, a
(38°582 143 N, 6°332 394 W, 225 m asl, Datum WGS84), 37 km
measure assigned to level 9 indicates the highest contribution
E of Badajoz (SW Spain). Its area is H" 33 ha. Seventy geo-
to soil fertility potential.
referenced soil samples were taken from the top layer
(0 20 cm), using a stratified random sampling scheme.
The data are arranged in matrix form, where the rows are the
A more detailed description of the characteristics of the
locations where soil were taken and the columns the soil
experimental field and the soil sampling can be obtained in
properties. Each cell can be represented by Xij, where i varies
Moral et al. (2011).
from 1 to 5 (soil properties) and j from 1 to 70 (sampling loca-
tion), and its value reflects the category. One possible way of
For each soil sample, the particle-size distribution was deter-
obtaining a ranking is to sum the categories of all the soil
mined by gravitational sedimentation using the Robinson
properties for each sampling location, and of all the sampling
pipette method (Soil Conservation Service, 1972), after
location for each soil property, i.e., summing by rows or by
passing the fine components through a 2 mm sieve, and
columns. However, these sums establish separate rankings
ECa-30 and ECa-90 data for all locations were obtained
for the sampling locations and the soil properties, and the
from kriged maps (after fitting a spherical variogram, with
procedure does not discriminate between ranking sampling
range = 288.4 m, sill = 0.505, nugget effect = 0.093, to the
locations in terms of soil properties and soil properties in
experimental one, and using the ordinary kriging algorithm),
terms of sampling locations.
previously generated from different transects of the measure-
ments of soil apparent electrical conductivity which were car-
The Rasch model uses the traditional total score (the sum of ried out using a direct contact sensor (Moral et al., 2010).
the item ratings) as a starting point for estimating response
probabilities. The model is based on the simple idea that WINSTEPS v. 3.69 computer program was employed to
some items (in this case study soil properties) are more conduct the formulation of the rating scale Rasch model
© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.plant-soil.com
J. Plant Nutr. Soil Sci. 2012, 000, 1 8 Analysis of soil fertility and its anomalies 3
(Linacre, 2009). To do that, firstly, a transformation of the soil
3 Results and discussion
properties measures to common categories was performed
and data were arranged in a matrix whose rows are the soil
3.1 Data response to the model
samples and columns are the soil properties (Tab. 1). For soil
texture properties, according to the characteristics of the
The contribution of the soil properties considered, in this case
experimental field, the ideal percentage of each texture class
study clay, silt, and sand contents, ECa-30 and ECa-90, to
was about a third of the total; in consequence, for an interval
obtain a representative measure of soil fertility potential at
H" 33% of clay, silt, or sand content the maximum categorical
each sampling location was performed with the formulation of
value, 5, was assigned. For ECa-30 and ECa-90, the highest
the Rasch model through the stages displayed in Fig. 1.
categorical values correspond to the classes with highest
measures. The other categories were associated with
classes in which their amplitude depends on the maximum
and minimum values of each soil property. The assignment of
categorical values across properties measures are displayed
in Tab. 2.
With 5 soil properties taken into account, the highest possible
raw score for the soil samples is 25 (the most potentially
fertile) and the lowest possible score is 0 (the least potentially
Figure 1: Diagram of the phases involved in the formulation of the
fertile).
Rasch model.
As outputs of the program, the empirical hierarchy of soil
After processing the matrix of categorical values by the WIN-
properties is illustrated using variable map and related to all
STEPS program, the output was several results with table or
soil samples, with each reported in logits, the statistics show
diagram format. The first information to be taken into account
how well the data fit the model and, additionally, soil sample
is if the data fit the model reasonably. To do this, the Infit and
and property misfits are explained.
Outfit statistics have to be analyzed. Thus, according to the
Infit and Outfit MNSQ values contained in Tabs. 3 and 4, 0.96
Table 1: Matrix of categorical values used to perform the formulation
and 0.97, there is a clear evidence about the agreement be-
on the Rasch measurement model.
tween the data and the model. Moreover, the mean standar-
dized (ZSTD) Infit and Outfit, which are the sum of squares
Sample Clay Sand Silt ECa-30a ECa-90
standardized residuals given as a Z-statistics (Edwards and
1 4 3 3 4 4
Alcock, 2010), are expected to be 0, being in this study  0.2
2 3 3 3 3 3 for samples and for items (Tabs. 3 and 4), denoting that the
data fit the model better than expected.
3 4 3 3 5 4
4 4 4 3 5 5
Another parameter to be considered is the standard deviation
... ... ... ... ... ...
of the Infit MNSQ (Bode and Wright, 1999), which is an index
of the overall misfit for soil samples and properties (a value
67 3 2 3 2 3
< 2 is considered acceptable). There is not important misfits
68 3 3 3 3 3
in this case study because their values are 0.75 and 0.15 for
69 3 2 2 4 4
soil samples and properties, respectively, also indicating an
acceptable overall fit of the data.
70 2 5 3 5 5
a
ECa-30, soil apparent electrical conductivity, 0 30 cm depth;
With the aim of estimating the internal consistency of soil
ECa-90, soil apparent electrical conductivity, 0 90 cm depth.
samples and properties, in the sense of determining the
Table 2: Soil properties measures recoded into rating scale categories.
Rating scale value 1 2 3 4 5
Clay / % < 13.8 or > 52.8 (13.8 19.4] or (19.4 25.0] or (25.0 30.5] or (30.5 36.1)
[47.2 52.8) [41.7 47.2) [36.1 41.7)
Sand / % > 70.4 < 6.9 or [59.8 70.4) (6.9 17.4] or (17.4 28.0] or (28.0 38.6)
[49.2 59.8) [38.6 49.2)
Silt / % < 7.8 or [58.9 66.1) (7.8 15.1] or (15.1 22.4] or (22.4 29.7] or (29.7 37.0)
[51.6 58.9) [44.3 51.6) [37.0 44.3)
ECa-30a / mS m 1 (3.46 7.36] (7.36 11.26] (11.26 15.16] (15.16 19.05] (19.05 22.95]
ECa-90 / mS m 1 (18.81 29.59] (29.59 40.37] (40.37 51.15] (51.15 61.93] (61.93 72.71]
a
ECa-30, soil apparent electrical conductivity, 0 30 cm depth; ECa-90, soil apparent electrical conductivity, 0 90 cm depth.
© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.plant-soil.com
4 Moral, Rebollo, Terrón J. Plant Nutr. Soil Sci. 2012, 000, 1 8
Table 3: Overall model fit information. Summary of all soil samples (70).
Total scorea Count Measure Model error Infit MNSQ Infit ZSTD Outfit MNSQ Outfit ZSTD
Mean 17.3 5 0.77 0.57 0.96  0.2 0.97  0.2
Standard Deviation 3.9 0 1.21 0.06 0.75 1.3 0.76 1.3
Maximum 23.0 5 2.69 0.79 3.33 2.6 3.32 2.6
Minimum 7.0 5  2.88 0.53 0.11  2.7 0.11  2.7
a
Total score, sum of points of the common scale considering all soil properties; count, soil properties taken into account; measure, logit position
of the soil; properties along the straight line that represents the latent variable, soil fertility potential; model error, standard error of
measurement; Infit and Outfit MNSQ, mean-square fit statistics to verify if items fit the model; Infit and Outfit ZSTD, standardized fit statistics to
verify if items fit the model.
Table 4: Overall model fit information. Summary of all soil properties (5).
Total scorea Count Measure Model error Infit MNSQ Infit ZSTD Outfit MNSQ Outfit ZSTD
Mean 242.2 70.0 0.00 0.15 0.97  0.2 0.97  0.1
S.D. 18.6 0 0.42 0.00 0.15 1.0 0.19 1.2
Max. 262.0 70.0 0.57 0.16 1.23 1.4 1.26 1.6
Min. 217.0 70.0  0.45 0.15 0.75  1.6 0.73  1.8
a
Total score, sum of points of the common scale considering all soil samples; count, soil samples taken into account; measure, logit position of
the soil samples along the straight line that represents the latent variable, soil fertility potential; model error, standard error of measurement; Infit
and Outfit MNSQ, mean-square fit statistics to verify if items fit the model; Infit and Outfit ZSTD, standardized fit statistics to verify if items fit the
model.
degree to which measures are free from error and yield con- no a general rule to initially define the correct number of cate-
sistent results, there is a reliability statistics. A better reliability gories. Thus, in this case study, a previous analysis was car-
is obtained when this statistics is close to 1; acceptable val- ried out with 10 categories, finding some results which indi-
ues would be > 0.7 (Sekaran, 2000). In this study, reliability cate that this number was not adequate, i.e., the  observed
was 0.77 and 0.87 for soil samples and properties, respec- average and the  structure calibration did not increase by
tively; thus, the consistency of data is adequate and probably category value, and some Infit and Outfit MNSQ values were
measures have not significant errors. out of the recommended range. However, data fit the model
reasonably, since the Infit and Outfit MNSQ values were be-
tween 0.98 and 1, and reliability was 0.80 and 0.87 for soil
When the assignment scale was checked to verify how it has
samples and properties, respectively. Although the optimum
been utilized, according to Linacre (2009), there was a strong
number of categories was not 10, the study could have
evidence to assert it was properly designed, with 5 cate-
continued (Moral et al., 2011).
gories: the  observed average and the  structure calibration
increase by category value, the Infit and Outfit MNSQ values
are between 0.6 and 1.5, and the  observed average values As it was previously indicated, with 5 categories the response
are similar to the  sample expected ones (Tab. 5). There is scale use is more adequate. This was also checked with an
Table 5: Response scale use.
Category Observed Observed Sample Infit Outfit Structure
counta average expected MNSQ MNSQ calibration
1 17  1.25  1.73 1.47 1.39 None
2 51  0.26  0.42 1.20 1.24  2.13
3 115 0.29 0.51 0.78 0.71  0.75
4 88 1.19 1.29 1.33 1.32 1.18
5 79 2.08 1.86 0.66 0.70 1.70
a
Observed count, number of times the category was selected considering all samples and soil properties; observed average, mean value of
logit positions modeled in the category; sample expected, optimum values of the average logit positions for the data; Infit and Outfit MNSQ,
mean-square fit statistics to verify if items fit the model; structure calibration, logit calibrated difficulty of the step representing the transition
points between one category and the next.
© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.plant-soil.com
J. Plant Nutr. Soil Sci. 2012, 000, 1 8 Analysis of soil fertility and its anomalies 5
additional tool, the probability curves, which represent the 0.6 and 1.5, and the Infit and Outfit ZSTD between  3 and 2.
likelihood of category selection against the Rasch measure. In this case study, all these values are in the proposed inter-
In Fig. 2, it can be seen that each category value is the most vals (Tab. 6), indicating that all considered soil properties
likely at some point on the continuum, i.e., all categories have have an important influence and support the soil fertility
been used, and there is not category inversions, i.e., a higher potential.
category is more likely at a higher point than a lower category
(for instance, if the Rasch measure is  1.5, the most likely
category assignment is 2, and if the Rasch measure is 1, the
3.2 Analysis of the Rasch measure: soil fertility
most likely category assignment is 3). Consequently, all cate-
potential
gories have been utilized and are behaving according to
expectation.
As an output of the Rasch model, all soil samples and their
properties are displayed in the same scale (Fig. 3). Thus, the
The final step consists in examining if each soil property fits relative distribution of the soil samples is provided in the
the general pattern of the model and contributes to support upper half of the continuum, according to the associated ferti-
the underlying latent variable, soil fertility potential. According lity potential, which has been achieved by means of the five
to Bode and Wright (1999), acceptable fit of each item soil properties taken into account (clay, silt, sand, ECa-30,
implies that the Infit and Outfit MNSQ should be between and ECa-90), and, similarly, the soil properties are provided
Figure 2: Probability curves for the five
categories considered in the case study.
Table 6: Item fit statistics. Influence of each soil property on the fertility potential in the experimental field (5 soil properties are considered).
Total Measure Infit Infit Outfit Outfit
Item Scorea MNSQ ZSTD MNSQ ZSTD
Silt 217 0.57 1.02 0.6 1.09 0.6
Clay 223 0.43 1.23 1.4 1.26 1.6
Sand 251  0.19 0.75  1.6 0.73  1.8
ECd 258  0.36 0.91  0.5 0.87  0.70
ECs 262  0.45 0.93  0.4 0.90  0.70
Mean 242.2 0.00 0.97  0.2 0.97  0.2
S.D. 18.6 0.42 0.15 1.0 0.19 1.2
a
Total score, sum of points of the common scale for each soil property considering all samples (70); measure, position of each soil property
along the straight line that represents the latent variable, soil fertility potential; Infit and Outfit MNSQ, mean-square fit statistics to verify if items
fit the model; Infit and Outfit ZSTD, standardized fit statistics to verify if items fit the model.
© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.plant-soil.com
6 Moral, Rebollo, Terrón J. Plant Nutr. Soil Sci. 2012, 000, 1 8
measure, silt content, is the soil property that less influence
exerts on soil fertility potential. This is in accordance with
some previous works (Moral et al., 2010, 2011).
Therefore, the establishment of a ranking according to prop-
erties of the soil samples should be fundamental in establish-
ing a crop in a field, since the most suitable conditions of soil
fertility can be expected in areas where soil samples have
Figure 3: Soil samples and properties in the same scale. The straight
achieved higher measure.
line represents the latent variable: soil fertility potential. Distribution of
soil samples (points) is above the line: to the right those more
potentially fertile; to the left those less potentially fertile. Soil
3.3 Misfit analysis: anomalies in soil fertility
properties are below the line: to the right less common (rare)
properties, with lower influence on soil fertility; to the left more potential
common (frequent) properties, with higher influence on soil fertility.
Results obtained after applying the Rasch model allow us to
ECd and ECs are deep (ECa-90) and shallow (ECa-30) soil apparent
electrical conductivity, approximately 0 90 and 0 30 cm depths, detect the soil samples which do not follow the general pattern
respectively.
(misfits). From a quantitative point of view, it can be found those
that do not endorse the model, or do not reach expected levels,
in the lower half of the diagram, classified according to the
because the measure is low (negative residuals) or high
fertility-potential measure of the soil samples.
(positive residuals). Misfits can be analyzed from the soil-
properties point of view, determining the soil samples which
The soil property that obtained the highest measure, and is to show distortions in any property with respect the general cri-
the right in the continuum (Fig. 3), is the silt content (measure = teria of all other samples, or from the soil-samples perspec-
0.57; see Tab. 6). This means it is the less common soil property. tive, analyzing in which soil property misfit occurred.
It can be seen in Tab. 6 that silt soil content is the property that
exerts the lowest influence on soil fertility; its raw score was the
Taking into account the soil properties, positive misfits are
lowest. At the other extreme, to the left, both ECa-30 and
found in those soil samples with higher fertility potential than
ECa-90 are situated (measure =  0.45 and  0.36, respectively;
it can be expected, according to the overall measure of all
see Tab. 6). They are the more common soil properties because
processed data. Negative misfits correspond to the soil sam-
most soil samples reach an optimum level of them. According to
ples that attain a lower level of fertility potential than it is
Tab. 6, ECa-30 and ECa-90 have the highest raw score and
expected for their position in the ranking. In this study, misfit-
the lowest measure. Almost all soil samples are influenced by
ting samples were only found for one soil property: clay con-
ECa-30 and ECa-90, both being the most influential proper-
tent. Two misfitted soil samples had a negative sign (Tab. 7).
ties on the soil fertility in the experimental field.
This is due to the fact that they are samples that even though
they have obtained a high score in the ranking, they do not
Analysis of Fig. 3 displays a continuous distribution of soil contain an adequate clay percentage, i.e., it was expected
samples, with most of them aggregated. However, some of they would have had a more adequate clay content, concre-
them, located to the left in the continuum, have very low tely their score should be 3. Moreover, these misfitted soil
score, denoting their low fertility potential. But, as it was pre- samples have the highest scores in ECa-30 and ECa-90 and
viously indicated, a majority of soil samples, located to the vice versa, which was not expected. The two samples with
right, has adequate properties or propensity for inducing soil positive misfits obtained a very low score in the ranking, but
fertility. A ranking of all soil samples according to their soil fer- they had an adequate percentage of clay, which was not
tility potential, their Rasch measure, can be obtained, indicat- expected. It is curious to denote that these soil samples,
ing where the most suitable places for crops are located, unlike the previous ones, have a very low score in ECa-30
while, on the contrary, those which got lower measure, being and ECa-90, so they do not follow the expected pattern, that
potentially less fertile, are also determined. In this case study, is, higher clay content would have led to higher ECa-30 and
no sample reached the maximum score of 25 points, ECa-90. In fact, the score for both samples is two units lower
although three samples reached 23 points and some of them than it is expected. The remaining 66 soil samples follow the
have more than 20 points, obtaining in consequence a high expected pattern, i.e., higher clay content leads to higher
Rasch measure and denoting good conditions to be poten- ECa-30 and ECa-90, usual in these soils (Moral et al, 2010).
tially very fertile; the minimum score was only 7 points.
From the soil-samples perspective, eight samples displayed
Another ranking of all considered soil properties have been misfit at least in one soil property (Tab. 8). Sample 56 was the
obtained as an output of the Rasch model. According to the worst case, showing three misfits, for clay content, ECa-30,
order established after processing all data, silt soil content is and ECa-90. The clay content has a positive residual where-
the property with higher measure, followed by clay content, as the ECa-30 and ECa-90 have negative residuals, so it cor-
later, sand content and, finally, ECa-30 and ECa-90. Thus, responds to a location that does not follow the expected pat-
the influence of each soil property on soil fertility potential in tern previously indicated, i.e., higher clay content corre-
the experimental field has been obtained. Soil properties with sponds with higher ECa-30 and ECa-90. Samples 5 and 51
lower measure, ECa-30 and ECa-90, have the greatest influ- have a very low score in clay content, but in ECa-30 and
ence on soil fertility potential; in contrast, the one with higher ECa-90 the score is high, so they display a negative residual
© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.plant-soil.com
J. Plant Nutr. Soil Sci. 2012, 000, 1 8 Analysis of soil fertility and its anomalies 7
Table 7: Misfits for clay content. The score indicates the points for each soil sample considering only this soil property, clay content. Positive
and negative misfits are indicated by the sign.
Soil sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Score 4 3 4 4 1 2 4 2 3 4 2 3 4 4 4
Misfit  2
Soil sample 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Score 3 3 2 3 4 4 4 4 3 4 2 5 3 4 4
Misfit
Soil sample 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
Score 2 4 3 3 3 3 4 3 4 3 4 4 3 3 4
Misfit 2
Soil sample 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Score 3 2 2 4 3 1 3 2 3 3 4 3 3 3 3
Misfit  2 2
Soil sample 61 62 63 64 65 66 67 68 69 70
Score 3 3 2 4 4 4 3 3 3 2
Misfit
Table 8: Misfits for those soil samples in which they have been
would have led to higher ECa-30 and ECa-90 (Moral et al.,
computed. The score indicates the points for each soil property.
2010), similar to the relationship between clay content and
Positive and negative misfits are indicated by the sign.
ECa-30 and ECa-90. Just the opposite, sample 13 has a neg-
ative residual in silt content because its score is too low for its
Clay Sand Silt ECa-30a ECa-90 Sample
ECa-30 and ECa-90 levels. The last misfit is related to the
Score 4 3 3 1 1 56
sand content in sample 26. It is higher than expected, prob-
Misfit 2  2  2 56 ably due to the particular condition at this location. In this
case study, only 8 of 70 samples, H" 10%, show some misfit,
Score 2 3 4 1 1 48
denoting how the overall fit of the data to the model is quite
Misfit 2 48
good, as it was initially checked.
Score 1 5 2 5 5 5
Misfit  2 5
The misfit analysis is an important tool to find the locations
where an anomaly exists and is also useful to find the main
Score 1 5 2 5 5 51
deficiencies of any soil property which could more notably
Misfit  2 51
affect soil fertility potential. When this information is introduced
Score 3 3 4 2 1 57
in a GIS, we can visualize the locations where misfits are appar-
Misfit 2 57
ent and analyze their patterns, if they exist. Moreover, com-
parisons between different soil samples, and consequently
Score 4 3 1 5 5 13
between different locations, and also site-specific amend-
Misfit  2 13
ments of any soil property with inadequate levels can be car-
Score 2 5 3 2 3 26
ried out, which could lead to higher soil fertility potential.
Misfit 2 2 26
Score 3 1 1 2 2 33
In Fig. 4, locations where soil-clay-content misfits exist are
shown; the two positive and negative misfits are both located
Misfit 2 33
together, denoting there is an excess of this textural property
a
in one zone of the field and a shortage of the same property
ECa-30, soil apparent electrical conductivity, 0 30 cm depth;
ECa-90, soil apparent electrical conductivity, 0 90 cm depth. in the other zone, with respect to the optimum level to reach a
higher soil fertility potential. If it is necessary, any work to
in clay content because their values are not according to the
amend this soil property should be conducted in these zones.
model. However, on the contrary, sample 33 has a positive
misfit in clay content because a lower value was expected
4 Conclusions
due to its low ECa-30 and ECa-90.
The successful formulation of the Rasch model with the aim
Another group of misfits is related to the silt content. Two of estimating soil fertility potential is the novel aspect of this
samples, 48 and 57, have positive residuals in silt content; work. It has been determined that the data reasonably fit the
they do not follow the expected pattern that higher silt content model and all considered soil properties (particle-size distri-
© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.plant-soil.com
8 Moral, Rebollo, Terrón J. Plant Nutr. Soil Sci. 2012, 000, 1 8
Acknowledgments
The authors acknowledge financial support from the Junta de
Extremadura (Project GR10038-Research Group TIC008,
co-financed by European FEDER funds).
References
Bode, R. K., Wright, B. D. (1999): Rasch Measurement in Higher
Education, in Smart, J. C., Tierney, W. G. (eds.): Higher Education:
Handbook of Theory and Research, vol. XIV. Agathon Press, New
York.
Bond, T. G., Fox, C. M. (2007): Applying the Rasch Model: Funda-
mental Measurement in the Human Sciences. 2nd edn., Lawrence
Erlbaum Associates, Inc., Mahwah, NJ, USA.
Edwards, A., Alcock, L. (2010): Using Rasch analysis to identify
uncharacteristic responses to undergraduate assessments. Teach.
Math. Applic. 29, 165 175.
Linacre, J. M. (2009): WINSTEPS (Version 3.69) [Computer
Program]. John M. Linacre (Ed.). Chicago, USA.
Moral, F. J., Álvarez, P., Canito, J. L. (2006): Mapping and hazard
assessment of atmospheric pollution in a medium sized urban
area using the Rasch model and geostatistics techniques. Atmos.
Environ. 40, 1408 1418.
Moral, F. J., Terrón, J. M., Marques da Silva, J. R. (2010): Delineation
Figure 4: Misfits for clay content in the experimental field.
of management zones using mobile measurements of soil
apparent electrical conductivity and multivariate geostatistical tech-
niques. Soil Till. Res. 106, 335 343.
bution and soil apparent electrical conductivity) have an
Moral, F. J., Terrón, J. M., Rebollo, F. J. (2011): Site-specific
important influence on soil fertility.
management zones based on the Rasch model and geostatistical
techniques. Comp. Electron. Agric. 75, 223 230.
After applying the Rasch method, a classification of all soil
Morari, F., Castrignanò, A., Pagliarin, C. (2009): Application of multi-
samples according to their soil fertility potential was obtained.
variate geostatistics in delineating management zones within a
The importance of soil apparent electrical conductivity to
gravelly vineyard using geo-electrical sensors. Comp. Electron.
properly characterize soil fertility in an agricultural field was
Agric. 68, 97 107.
also highlighted.
Rasch, G. (1980): Probabilistic Models for Some Intelligence and
Other useful results are those related to the misfits, which Attainment Tests. Revised and expanded edition, University of
enable to establish those soil samples which have any anom- Chicago Press, 1960, Denmark, Chicago, USA.
aly. In the case study, some samples have disproportionate
Ren, W., Bradley, K. D., Lumpp, J. K. (2008): Applying the Rasch
content of some soil textural components which, in turn,
model to evaluate an implementation of the Kentucky Electronics
affect the ECa-30 and ECa-90 values.
Educations Education Project. J. Sci Educat. Technol. 17,
618 625.
This information is very important from an agronomic per-
Sekaran, U. (2000): Research Methods for Business: A Skill Building
spective because not only locations in the experimental field
Approach. John Wiley and Sons Inc., Singapore.
with high soil fertility potential can be determined but also
Smith, R. M. (1996): Polytomous mean-square statistics. Rasch
those locations where any anomaly exists. Furthermore,
Measurem. Trans. 6, 516 517.
using a GIS, these places can be visualized and delimited
which is useful to make decisions regarding fertilization and
Soil Conservation Service (1972): Soil Survey Laboratory. Methods
site-specific amendments of any soil property with inade- and Procedures for Collecting Soil Samples. Soil Survey Report 1,
quate levels with respect to soil fertility potential. USDA, Washington DC, USA.
© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.plant-soil.com