Binary logistic regression—Instrument for assessing museum indoor air impact on exhibits

ABSTRACT

This paper presents a new way to assess the environmental impact on historical artifacts using binary logistic regression. The prediction of the impact on the exhibits during certain pollution scenarios (environmental impact) was calculated by a mathematical model based on the binary logistic regression; it allows the identification of those environmental parameters from a multitude of possible parameters with a significant impact on exhibitions and ranks them according to their severity effect. Air quality (NO₂, SO₂, O₃ and PM_2.5) and microclimate parameters (temperature, humidity) monitoring data from a case study conducted within exhibition and storage spaces of the Romanian National Aviation Museum Bucharest have been used for developing and validating the binary logistic regression method and the mathematical model. The logistic regression analysis was used on 794 data combinations (715 to develop of the model and 79 to validate it) by a Statistical Package for Social Sciences (SPSS 20.0). The results from the binary logistic regression analysis demonstrated that from six parameters taken into consideration, four of them present a significant effect upon exhibits in the following order: O₃>PM_2.5>NO₂>humidity followed at a significant distance by the effects of SO₂ and temperature. The mathematical model, developed in this study, correctly predicted 95.1 % of the cumulated effect of the environmental parameters upon the exhibits. Moreover, this model could also be used in the decisional process regarding the preventive preservation measures that should be implemented within the exhibition space.

Implications: The paper presents a new way to assess the environmental impact on historical artifacts using binary logistic regression. The mathematical model developed on the environmental parameters analyzed by the binary logistic regression method could be useful in a decision-making process establishing the best measures for pollution reduction and preventive preservation of exhibits.

Introduction

The idea that is easier to prevent than to restore has gained more ground in the last decades, so the preventive preservation principles have been accepted and applied in museums all over the world. In this sense, a special attention has been given to the microclimate parameters and indoor air quality. The adverse effects of high temperature and humidity (RH) on museum exhibits are unanimously recognized, as well as their fluctuation (Sciurpi et al., 2015; D’agostino et al., 2015; Corgnati et al., 2009; Rose et al., 1995; Krupińska et al., 2013); stable humidity values (around 50%) as well as low and stable values of temperature represent the optimal preservation conditions. On the opposite, a high value of the humidity favor mold development (Anaf et al., 2013; Janssen and Christensen, 2013) and could represent a favorable environment that accelerate the degradation of artifacts. Moreover, the destructive effect could be accelerated by the high concentrations of gaseous compounds from indoor air (Godoi et al., 2013; Saraga et al., 2011); for example, the sulfur and nitrogen oxides could directly react with materials of the artifacts, damaging them. This harmful effect could be amplified in the presence of humidity (Kontozova-Deutsch et al., 2011) and metal cations—catalysts of oxide transformation, in strong and corrosive acids (Loupa et al., 2007; Kontozova-Deutsch et al., 2011; Chianese et al., 2012). According to Thomson (1986), the light could be more harmful on the artifacts than temperature due to its direct impact and photochemical reactions. In consequence, the measure of reducing the artifacts’ exposure to natural or artificial light has been already implemented in museums (Ayres et al., 1990).

Moreover, the presence of ozone inside museums, in concentrations over the recommended limits, could accelerate the reactions of the oxides to form acids and interact with the organic compounds from paint composition, inducing colors changes or pigments discoloration (Salmon et al., 2000; Cavicchioli et al., 2012). The deposition of suspended particles on the surface of artifacts could damage them and change their feature (Anaf et al., 2013; Grau-Bové and Strlič, 2013). Furthermore, the presence of humidity and other gaseous compounds in the air could generate electrochemical corrosion cells and damage the artifacts’ surfaces.

The identification and quantification of the chemical compounds and microclimate parameters that could influence the integrity of the artifacts represent the first step in the process of preventive conservation. Useful information regarding the environmental quality conditions inside museums could be obtained only by a long-term monitoring of the air quality and microclimate parameters. The indoor/outdoor (I/O) ratio is one of the most used indicators to predict the outdoor air influence on the indoor air quality and to identify the inside pollution sources. Supplementary information could be obtained through correlation and regression analyses of the monitored parameters; thus, Chen and Zhao (2011) used a linear regression method to compute the infiltration factor (F_in) of particulate matter from outdoors and to identify the existence of indoor pollution sources.

But in recent years, the logistic regression (LR) analysis was used more and more in various research studies as a method that uses numerical and categorical variables and where the dependent variable is categorical. Initially, the method has been successfully used in medicine and epidemiology to analyze the risk factors associated with early diagnostics (Callas et al., 1998; Wang et al., 2002; Reisner et al., 2015; Hailpern and Visintainer, 2003; Whittemore and Halpern, 2003). But, in time, the utility of this method was expanded to other areas such as sociology, tourism, economy, etc. For instance, the logistic regression was used by Grigolon et al. (2014) to analyze the housing satisfaction from a series of sociodemographic and urban characteristics: sex, age, household composition, urbanization level, and income. At the same time, Frangos et al. (2015) used it to identify the predictive factors of tourist loyalties to Athens. Notario del Pino and Ruiz-Gallardo (2015) applied the LR to predict “the fire-induced soil water erosion degree,” taking into consideration some topographic and climatic data and the fires severity. Using the same method, Conoscenti et al. (2015) assessed an earth-flow susceptibility based on some specific lithologic area and climatological information. The applications of LR could be found in the economic-financial field, too. Irimia-Dieguez et al. (2015) have developed a mathematical model for the economic-financial analysis of the small and medium enterprises starting from nonfinancial and macroeconomic variables.

To our knowledge, this is the first study where the influence of the environmental conditions on museum artifacts was assessed using the binary logistic regression method. The results of binary logistic analysis allowed us (i) to identify the parameters with a significant impact on the artifacts; (ii) to classify these parameters based on their severity potential effect; (iii) to elaborate a mathematical model to predict the effect of a pollution context on the artifacts; and (iv) to validate the mathematical model.

The binary logistical regression method was applied to evaluate the indoor museum air quality impact on exhibits of the Romanian National Aviation Museum. Data were collected during two periods of time in summer 2014 and winter 2015.

Materials and methods

Measurement site

Romanian National Aviation Museum in Bucharest is situated in a northern part of the city, in the old Pipera military aerodrome hangars, in reach of green vegetation area and far away from important city routes and important industrial pollutant sources (Figure 1a).

Figure 1. Location of Romanian National Aviation Museum in Bucharest (a); museum exhibits (b).

The museum’s exhibition space has two hangar buildings and an outdoor exhibition area. Hangar 1 hosts the main exhibition—aeronautics history from the beginnings to 1959, and in Hangar 2 can be seen airplanes, flight simulators, antiaircraft and radiolocation techniques from the 1960s until today. The majority of exhibits are made of various metals protected with surface layers with wood or plastic material, glass, skin, and latex components (Figure 1b).

In spite of the fact that this building was not designed to be a museum, the inside spaces have been accommodated for exhibitions and storage. Hangars were built with usual bricks and have metal doors and windows that are not airtight and allow an airflow from outside the building. There are no acclimatization systems, and the ventilation is performed by opening the windows and the doors, when necessary. For the cold season, the spaces are connected to the city centralized heating system. In the rainy season, there are identified high-humidity areas inside the building.

The case study, presented in this work, was based on the monitoring data from Hangar 2.

Data collection, quality control (QC), and quality assurance (QA)

In order to monitor the air quality from inside museum and to identify the pollution sources, we analyzed chemical pollutants and microclimatic parameters from outside and inside the building during two periods: summer 2014 (9–17 July 2014) and winter 2015 (23 February–20 March 2015). The following microclimate parameters were monitored: temperature, humidity, and chemical compounds that could react with most metal exhibits, because nitrogen dioxide (NO₂) and sulfur dioxide (SO₂) in the presence of water form highly corrosive acids; ozone (O₃) and fine particulate matter (aerodynamic diameter ≤2.5 μm; PM_2.5) particles in the presence of water could induce chemical oxidation and electrochemical reactions. It should be mentioned that these compounds present in high concentrations in the urban air, due to traffic, could contaminate the museum indoor air.

The level of light radiation was not monitored because exhibition areas have curtains at windows to block the natural light, and the artificial light was used for short periods of time.

The measurements of NO₂, SO₂, and O₃ concentrations from the air were performed by an auto-laboratory equipped with automated analyzers: Horiba APNA 370 for NO₂, Horiba APSA 370 for SO₂, and Horiba APOA 370 for O₃ (Horiba Ltd., Kyoto, Japan) coupled with a programmable indoor/outdoor commutation system. The detection limits of these three equipments, calculated as 3 times the standard deviation of zero gas, were 0.75 µg/m³ for NO₂, 1.25 µg/m³ for SO₂, and 1 µg/m³ for O₃. The measurements were carried out in compliance with the standard method requirements: SR EN 14211:2012 for NO₂, SR EN 14212:2012 for SO₂, and SR EN 14625:2012 for O₃ (Romanian Association for Standardization, 2012a, 2012b, 2012c). For quality assurance purpose, the analyzers were calibrated and checked periodically using certified pressure gas cylinders. The analyzers were equipped with a storage data system that allowed the data recording, storage, and (pre)processing. The outdoor temperature and humidity were measured with a meteorological station MetPak (Gill Instruments Limited, Lymington, Hampshire, UK) mounted on the auto-laboratory and indoor data were collected with an analyzer WolfSense 2010 (GrayWolf Sensing Solutions, Shelton, Connecticut, USA).

PM_2.5 concentrations were determined by gravimetric method according to SR EN 12341:2014 (Romanian Association for Standardization, 2014). The particles were retained on cellulose esters filters (Ø: 47 mm; Millipore, Darmstadt, Germany; type: 0.8 μm, white) using Leckel Sven Ingenieurbüro GmbH (Berlin, Germany) samplers. Daily samples were taken at a flow rate of 2.3 m³/hr. Before and after sampling, all filters were conditioned for 48 hr in a climatic chamber (HPP 108; Memmert GmbH, Schwabach, Germany) in constant temperature (20 ± 0.5 °C) and relative humidity (50 ± 5%), then weighted with an analytical balance (AG 135; Mettler-Toledo GmbH, Greifensee, Switzerland) with 10 µg resolution. The weight gain of the filters represented the mass of PM_2.5 from the volume of air sampled; the concentration of PM_2.5, expressed in μg/m³, was determined by dividing the mass of particles (μg) by the volume of air sample (m³).

Indoors, samplers and automatic analyzers were installed in the middle of the room, and outdoors, the mobile laboratory was placed 5 m from the building, away from the access roads.

For quality assurance of PM_2.5 determination, the analytic balance was calibrated daily, before weight measurements, using a 0.1 g certified standard weight. Sampling flow was verified weekly with a calibrated flow meter (Defender 510-M; Butler, New Jersey, USA).

Hourly data were recorded for NO₂, SO₂, O₃, and microclimatic parameters and daily data for PM_2.5.

The characterization of the monitoring data series, the data distribution, and the correlation and regression analyses were carried out using a Statistical Package for Social Sciences, version 20.0 (IBM, Armonk, NY, USA).

Developing the mathematical model to evaluate the environmental impact on the museum exhibitions

The regression is one of the most used methods to obtain the relationships between two or more predictor variables and a dependent variable. If all variables are numerical, the regression method used could be linear/nonlinear, simple/multiple. If the dependent variable is categorical, only the logistic regression method could be used. In our case, we used six numerical predictor variables (NO₂, SO₂, O₃, and PM_2.5 concentrations, as well as temperature and humidity) and a binary categorical variable (the effect on the exhibits), so we developed a mathematical model by binary logistic regression method.

The binary categorical variable appears when it belongs to two separated categories expressed by numeric values of 1 and 0; usually, 1 means the presence of an event, so it will represent the probability of an event happening based on the values of the predictor variables. In our case, the two categories represent the probability of the exhibits to be (1) or not to be (0) affected by the environmental conditions. The linear regression estimates the value of the dependent variable based on the values of the predictor variables, but the logistical regression gives information about a “transformation” of the dependent variable, logit(p):

(1)

where p is the probability of the museum exhibition to be affected by the environment and 1− p, the probability of not to be affected; and odds_ratio is the ratio of the two probabilities: p/(1 − p).

In the situation when we have k predictor variables, the general regression model will have the form:

(2)

where p is P(y = 1/x₁,x₂,…,x_k) and represents the probability that artifacts would be affected if the predictor variables x₁, x₂,…, x_k are taken into consideration.

The equation obtained by the binary logistic regression method gave information about

• the importance of each predictive variable based on the value of coefficients β_k; it is possible to establish a probable impact hierarchy of the monitored parameters on the exhibits.

• attributing a pollution situation in a category based on the probability values, P(y = 1/x₁,x₂,…,x_k), using the equation:

(3)

Binary logistic regression analysis was applied to results from Hangar 2 based on six predictive variables: concentrations of NO₂, SO₂, O₃, and PM_2.5 and the values of temperature and RH from indoor air.

The value 0 was assigned to the dependent variable (the environmental conditions do not affect the artifacts) only in the situation in which values of all parameters were smaller than the recommended limits by ASHRAE (American Society of Heating, Refrigerating and Air-Conditioning Engineers, 2007) for the general collections. Moreover, the dependent variable was assigned the value 1, if at least one parameter value was above the recommended limit value. Two methods could be used to identify the statistical not significant parameters and the computation of the β coefficient: the Enter method based on the Wald test and the forward stepwise likelihood-ratio (LR) method.

For this study, we used the Enter method (predictor variables are analyzed simultaneously), although the forward stepwise LR method allows both the elimination of not significant parameters and also the obtaining of the final β coefficient values for the significant parameters using a single compilation run. In this way, we could visualize (i) the values of the coefficient β for all six predictor variable; (ii) the elimination condition from the model for not statistically significant parameters; and (iii) the way in which the elimination of some parameters could affect the values of the β coefficient and the mathematical model precision.

For the model validation, we operated 79 combinations of parameters (10% from the total number) that have not been used for the mathematical model calibration. Binary logistic regression was made using Statistical Package for Social Sciences, version 20.0.

Results and discussion

Air quality monitoring results

The results of the air quality monitoring campaigns are presented in Table 1, which includes statistical test data from normality-checked data series distribution, I/O ratios, and the limit values, as well as air pollution concentrations and the values of microclimate parameters.

Table 1. Results of monitoring and indicators of data series such as central trend, dispersion, and distribution forms.

Indicator		NO2 (µg/m^3)			SO2, (µg/m^3)			O3 (µg/m^3)			PM2.5 (µg/m^3)			Temperature (°C)		RH (%)
		Indoor	Outdoor	I/O	Indoor	Outdoor	I/O	Indoor	Outdoor	I/O	Indoor	Outdoor	I/O	Indoor	Outdoor	Indoor	Outdoor
N	Valid	794	794		794	794		794	794		33	33		794	794	794	794
	Missing	0	0		0	0		0	0		0	0		0	0	0	0
Mean		12.3684	18.3897	0.92	4.0275	5.1742	0.84	10.7808	31.0482	0.35	9.8809	20.5072	0.49	12.9068	10.9626	57.8278	77.7409
Median		10.1900	12.4300		3.4800	4.3520		9.9650	31.1350		9.5400	20.1200		9.6000	8.0000	56.4000	80.4800
SD		7.23145	15.53057		1.23996	2.94485		1.86806	5.79900		1.31797	2.10373		6.94888	7.91563	7.69807	19.58626
Skewness		1.536	1.713		2.653	5.968		1.294	−0.147		0.564	−0.079		1.127	1.164	0.282	−0.505
SE of skewness		0.087	0.087		0.087	0.087		0.087	0.087		0.087	0.087		0.087	0.087	0.087	0.087
Kurtosis		2.578	3.200		11.201	54.141		0.956	−0.925		−0.927	−0.379		−0.554	0.147	−0.507	−0.827
SE of kurtosis		0.173	0.173		0.173	0.173		0.173	0.173		0.173	0.173		0.173	0.173	0.173	0.173
Minimum		2.98	0.78		2.93	3.13		8.42	19.90		7.98	15.42		4.20	0.30	37.80	30.00
Maximum		43.73	86.13		12.97	36.66		19.49	43.16		12.65	24.54		27.60	33.40	73.70	100.00
Percentiles	25	7.6200	7.6990		3.3175	3.5860		9.4500	26.5600		8.7800	19.0800		8.6000	6.2000	52.3000	63.0000
	50	10.1900	12.4300		3.4800	4.3520		9.9650	31.1350		9.5400	20.1200		9.6000	8.0000	56.4000	80.4800
	75	15.6600	24.0575		4.5850	5.8920		11.5100	35.4300		11.0400	22.4100		13.0250	12.2750	62.6000	98.0000
Kolmogorov–Smirnov Z		4.465	5.034		7.439	6.876		6.144	1.547		4.089	2.999		10.002	7.490	2.320	3.603
Asymptotic significance (two-tailed)		0.000	0.000		0.000	0.000		0.000	0.017		0.000	0.000		0.000	0.000	0.000	0.000
ASHRAE*		4–20	—		1–5.7	—		1–10	—		1–10	—		<25	—	25–75	—
Directive 2008/50/EC**		—	200		—	350		—	120		—	—		—	—	—	—
EPA***		—	—		—	—		—	—		—	35		—	—	—	—

*ASHRAE Handbook, Chapter 21, 2007, for the general collections, Class Control C for microclimate parameter.

**Directive 2008/50/EC on ambient air quality and cleaner air for Europe.

***U.S. Environmental Protection Agency National Ambient Air Quality Standard.

The ambient air quality was assessed by considering the limit values required in Directive 2008/50/EC for NO₂, SO₂, and O₃ (EU, 2008), and for the museum indoor air quality, values recommended by ASHRAE (2007) for general collections.

In addition, the PM_2.5 were analyzed by taken into consideration the 35 µg/m³ daily limit established by the U.S. Environmental Protection Agency (Esworthy, 2013), because European legislation established only an annual limit value.

In spite of the fact that Bucharest is one of the European capitals with high level of air pollution (Pascal et al., 2013), the data collected from the ambient air showed that the average and maximum values were under the imposed limit values for all indicators (NO₂, SO₂, O₃, and PM_2.5) according to the current environmental legislation for human health protection. These results could be explained by the fact that the museum area is located close to the city outskirt at a relative significant distance from any important pollution sources. Moreover, the studied area is surrounded by rich green vegetation, which leads to a reduction of the pollution level in the air (Cohen et al., 2014; Bealey et al., 2007; Beckett et al., 2000).

The concentrations of indoor air pollutants were compared with the ASHRAE (2007) recommended values for the general collections, and it was observed that, on average, only the O₃ concentration exceeded, by 8%, the recommended value. The concentrations of NO₂ and SO₂ were under those limit values, as well as PM_2.5, which was under the limit, but very close to the recommended value.

At first sight, the pollutant concentrations didn’t appear to be a hazard for the museum artifacts, but a more profound analysis based on variation ranges between values (minimum/maximum) and frequencies of exceeding limits (Table 2) pointed out a more complex situation. In this scenario, the NO₂ and SO₂ hourly average values were up to 15% of the time above the limits (13.5% of time for NO₂ and 9.4% for SO₂). In addition, PM_2.5 values were above the limit for 42.4% of the time and 48.6% for O₃ (Table 2).

Table 2. Frequency of data occurrence above suggested limit values.

Parameter	ASHRAE suggested limits	Below the suggested limits (%)	Above the suggested limits (%)
NO2	4–20 µg/m^3	86.5	13.5
SO2	1.14–5.7 µg/m^3	90.6	9.4
O3	1–10 µg/m^3	51.4	48.6
PM2.5	1–10 µg/m^3	57.6	42.4
Temperature	25 °C	89.7	10.3
RH	25–75%	100	0

In the case of microclimate parameters (temperature and RH), it was shown that 10% of temperature values exceed the limit of 25 °C, whereas the RH, on average, was within the required limits for the Class Control C (25% < RH < 75%). The frequency analysis (Table 2) showed that in 86% of the cases, the RH was higher than 50% and could affect the integrity of the artifacts (Thomson, 1994; Davis, 2006; Mecklenburg and Tumosa, 1999).

The daily maximum fluctuations of temperature (3.1 °C) and humidity (9.5%) weren’t considered a danger to this type of exhibits because for Control Class C, there are no recommended limits.

In this context, preventive preservation measures should be taken, such as reducing the pollutant concentrations in the air and maintaining under control the microclimate parameters.

The first steps towards solving the pollution problem could be the identification of pollution sources as well as ranking the pollutants and the microclimate factors as function of severity of their effects that might be induced upon the artifacts.

Identification of pollution sources

The computed values of the I/O ratio and statistical correlation analysis were used to identify the pollution sources as well as their contribution to the museum indoor air quality.

The statistical test results for checking the distribution normality of data series, more specifically the skewness, kurtosis, and Kolmogorov–Smirnof–Lillilefors test (Table 1), showed deviations from normal distribution in all data series. In this situation, we used Spearman’s correlation coefficients of ranks, q, to establish the correlation between parameters (Table 3).

Table 3. Spearman’s correlation coefficients for museum indoor (I) and outdoor (O) air quality parameters.

	I-NO2	O-NO2	I-SO2	O-SO2	I-O3	O-O3	I- PM2.5	O-PM2.5	I-temp	O-temp	I-RH	O-RH
I-NO2	1.000
O-NO2	0.789**	1.000
I-SO2	0.139**	0.000	1.000
O-SO2	0.256**	0.099**	0.800**	1.000
I-O3	−0.334**	−0.481**	0.595**	0.516**	1.000
O-O3	−0.425**	−0.654**	0.377**	0.401**	0.830**	1.000
I- PM2.5	−0.114**	−0.121**	0.373**	0.309**	0.263**	0.175**	1.000
O-PM2.5	−0.086*	0.026	−0.409**	−0.376**	−0.316**	−0.257**	−0.335**	1.000
I-temp	−0.151**	−0.161**	0.636**	0.439**	0.561**	0.379**	0.215**	−0.284**	1.000
O-temp	−0.005	−0.189**	0.676**	0.657**	0.749**	0.639**	0.238**	−0.338**	0.529**	1.000
I-RH	−0.098**	−0.012	−0.046	−0.200**	−0.160**	−0.210**	0.098**	0.107**	0.121**	−0.339**	1.000
O-RH	0.008	0.186**	−0.430**	−0.558**	−0.540**	−0.592**	−0.216**	0.310**	−0.237**	−0.590**	0.294**	1.000

Note. The coefficients that indicate good and very good significant statistical correlations are in bold font.

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

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

Results showed that correlation between outdoor and indoor data was very good (q_NO2 = 0.789; q_SO2 = 0.800; q_O3 = 0.830) for gaseous pollutant (NO₂, SO₂, and O₃) and good for temperature (q_temp = 0.529).

This indicated that outdoor air could be a possible pollution source for the museum indoor air. This hypothesis was confirmed by the values of NO₂ and SO₂ I/O ratios (I/O_NO2 = 0.92; I/O_SO2 = 0.84) and by the building-related specificities and configurations (direct access from the outdoor area, deficient sealed areas).

Smaller I/O ratios for O₃ and PM_2.5 (I/O_O3 = 0.35; I/O_PM2.5 = 0.49) could be explained by O₃ possible chemical and photochemical reactions and by a frequent elimination of particles through suction during the hygiene maintenance process. Moreover, due to a small number of visitors, there were no additional issues such as particle resuspension or a substantial contribution coming from visitors’ clothes and shoes.

Regarding the relative humidity, the high indoor values (RH >50% in 86% of the measurements) and the low correlation coefficient (q_RH = 0.294) indicated the possibility of supplementary indoor humidity sources that could influence the RH value. In those conditions, the outdoor air was the most important source of humidity and chemical pollutants for indoors. Besides the influence of the outdoor RH, it should also be taken into consideration the indoor RH sources (the humid areas inside the museum).

Statistical modeling

Binary logistic regression analysis was based on data obtained within the air quality monitoring process from Hangar 2 and it is presented in Table 1.

Out of 794 data combinations, 715 were used to calibrate the mathematical model; the remaining 79 combinations represented the necessary sample to validate the mathematical model. All six parameters: concentrations of NO₂, SO₂, O₃, and PM_2.5, temperature, and RH, were taken into consideration, and the dependent variable (categorical variable) was considered “the effect on the artifacts” and could have only two values, 1 or 0, as follows:

• 1, possible effect on the artifacts, if at least one of the values of those six parameters exceeded the ASHRAE (2007) recommended limits for general collections (20 µg/m³ for NO₂, 5.7 µg/m³ for SO₂, 10 µg/m³ for O₃, 10 µg/m³ for PM_2.5, 25 °C for temperature, and 25–75% for RH).

• 0, without effect on the artifacts, if the values of all six indicators were under recommended limits.

The results from the logistic regression analysis were used to identify the effect of each specific parameter upon the artifacts, their impact ranking, and the prognosis of cumulated effects on the artifacts. The prognosis of cumulated effects was based on the mathematical model obtained by replacing the β coefficient from eq 2 with the value obtained through the binary logistic regression analysis. In those conditions, eq 2 became

(4)

where β₁, …, β₆ are computed logistic regression coefficients using statistical software program, specifically the natural logarithms of the “odds_ratio” for each variable; β₀ represents the constant (similar liniar regression); and x_NO2, …, x_RH, represent the concentration values of NO₂, SO₂, O₃, and PM_2.5 as well as temperature and humidity values.

The values of the regression coefficients and their statistical significance obtained by Enter logistical regression method were included in Table 4.

Table 4. The binary logistic regression of the model—Enter method (first run).

Model summary
Step	−2 log likelihood	Cox and Snell R^2	Nagelkerke R^2
1	231.852^a	0.564	0.824

Classification table^b
			Predicted
			Effects on exhibits
Observed			.00	1.00	Percentage correct
Step 1	Effects on exhibits	0.00	176	13	93.1
		1.00	19	507	96.4
	Overall percentage				95.5

Variables in the equation
Parameter		β	SE	Wald	df	Significance	Exp(β)
Step 1^c	NO2	0.360	0.052	48.090	1	0.000	1.434
	SO2	0.472	0.767	0.379	1	0.538	1.604
	Temperature	−0.038	0.153	0.061	1	0.805	0.963
	RH	−0.081	0.025	10.302	1	0.001	0.922
	O3	6.102	0.689	78.484	1	0.000	446.565
	PM2.5	3.422	0.365	88.133	1	0.000	30.633
	Constant	−90.931	9.389	93.795	1	0.000	0.000

^aEstimation terminated at iteration number 10 because parameter estimates changed by less than 0.001.

^bThe cut value is 0.500.

^cVariable(s) entered in step 1: NO₂, SO₂, temperature, RH, O₃, and PM_2.5.

The logistic regression could use two indicators such as Cox and Snell R² and Nagelkerke R², the same as for coefficient r² from linear regression that estimates the contribution of predictor variable to the variability of dependent variable. We used the Nagelkerke R² indicator to analyze the contribution of all six predictor variables to the variability of the dependent variable. It has been unanimously recognized the fact that Cox and Snell R² indicator underestimates the real value. The test results (Table 4, Model Summary) based on the six predictor variables (NO₂, SO₂, O₃, PM_2.5, temperature, and RH) could explain in great proportion (82.4%) the effect of the environment on the artifacts.

The results from the classification table (Table 4) showed that the mathematical model predicts 95.5% of cases correctly, so we could conclude that it is a good performing model and its regression coefficients (β) are shown in “Variables in the equation” (Table 4).

The results from Wald test, also presented in Table 3, were useful for estimating which coefficients were statistically significant (significance < 0.05) and which were not statistically significant (significance > 0.05). Exp(β) represents “odds_ratio” for each predictor variable, specifically e^βi.

Six predictive variables were analyzed by regression analysis, but only four of them had a statistical significance: concentrations of NO₂, O₃, and PM_2.5 and RH. The remaining two predictive variables, temperature and concentration of SO₂, didn’t show a statistical significance (significance > 0.05), so they were discarded from the equation of mathematical model. In those conditions, the mathematical model (eq 4) became

(5)

The values of coefficient β₀, …, β₄ (Table 5) were obtained by repeating Enter method of binary logistic regression applied only on four statistical significant predictor variables. The elimination of two parameters from the analysis generated a slight decrease (from 95.5% to 95.1%) in the model accuracy.

Table 5. The results of binary regression model—Enter method (the second compilation run).

Variables in the equation
Parameter		B	SE	Wald	df	Significance	Exp(B)
Step 1^a	NO2	0.372	0.046	64.674	1	0.000	1.450
	RH	−0.083	0.025	10.929	1	0.001	0.921
	O3	6.169	0.674	83.872	1	0.000	477.720
	PM2.5	3.468	0.350	98.137	1	0.000	32.061
	Constant	−90.813	9.367	93.989	1	0.000	0.000

^aVariable(s) entered in step 1: NO₂, RH, O₃, and PM_2.5.

By introducing the regression coefficient β (0.372 for β₁; 6.169 for β₂; 3.468 for β₃; −0.083 for β_4; −90.813 for β₀) in eq 5, we obtained the following final form of the mathematical model:

(6)

from which

(7)

By introducing the value of odds_ratio in eq 1, we could compute the probability of the museum artifacts to be affected when the pollution was characterized by certain values for concentrations of NO₂, O₃, and PM_2.5 and humidity (RH).

The value of probability could be also computed using the same Statistical Package for Social Sciences (version 20.0) being used to validate the mathematical model by running the 79 data combinations that weren’t used within the model calibration process.

Following the validation process, only one result was wrong, but 78 results proved to be correct (98.7%), which were above the program computed accuracy range (95.1%).

The probability values could also be interpreted as a possible environment impact on the museum artifacts. In conclusion, to facilitate the interpretation, it could be introduced an impact assessment system based on the computed value of probability (p): (i) very low impact for probabilities ranging 0 < p < 0.2; (ii) low impact for probabilities ranging 0.2 < p < 0.4; (iii) moderate impact for probabilities ranging 0.4 < p < 0.6; (iv) strong impact for probabilities ranging 0.6 < p < 0.8 and v); and very strong impact for probabilities p > 0.8.

But the results of binary logistic regression could be used in a broad range of applications, not only for environmental impact assessment of the indoor air quality upon the artifacts. Starting from the coefficient regression values, a ranking of air pollution parameters could be established depending on their impact upon the exhibits, which actually allows an easier identification of measures that should be taken in order to reduce the impact. In our study, it seems that the most important parameter was the O₃ concentration, followed by PM_2.5 concentration, NO₂ concentration, and the level of humidity. The concentration of SO₂ and the temperature could affect to a lesser extent the exhibits. Throughout correlation analysis and I/O ratio values, it already had been established that the most important source of pollution was the outdoor air. In those conditions, a greater protection of the artifacts would be achieved by reducing the penetration of the polluted air from outside the building.

At the same time or equally important, it would be useful to identify and eliminate all possible humidity sources due to the noncompliant maintenance of the building.

Conclusion

The results obtained during this study demonstrated, one more time, the utility of the statistical analysis methods in interpretation of data series obtained throughout environmental parameters monitoring.

Generally, the linear regression and Pearson correlation analysis have been very frequently used in the environmental studies to identify the pollution sources and in the prediction studies, but this was the first study in Romania, to our knowledge, in which the binary logistic regression had been used to assess the effect of the environment upon the artifacts.

In conclusion, based on values of regression coefficients β and analysis of the statistical significance, it could be identified and ranked the pollution parameters with significant effect on the artifacts, allowing us to prioritize the pollution reduction measures and, subsequently, the cost estimation of those measures. At the same time, the developed mathematical model could be useful in identifying the potential effect of a certain pollution situation on artifacts. Moreover, by computing and assimilating the probability, p, as possible impact, it could be a useful indicator to evaluate the air quality of the storage and exhibition areas of designated national heritage objects.

The mathematical model, by simulation of some theoretical situations and analysis of the obtained results, could be useful in a decision-making process establishing the best measures for pollution reduction. Moreover, the information obtained by online monitoring of museum system could be integrated with a mathematical model to continuously and directly predict the cumulated effects of the environment upon the exhibits.

The mathematical model elaborated was built on the data obtained from monitoring the air quality and microclimate parameters of Hangar 2, so it was specific only to these conditions. On the other hand, the overall method could be used in other situations (case studies) in which it is possible to change the predictor variables (monitored parameters) and the criteria attributed to the two categories of variables linked to the new particular conditions.

We consider this paper as a starting point for the usage of the binary logistic regression in the evaluation process of the air quality and its impact on the museum exhibits. We hope that this method could be improved by other research groups and subsequently extending its applications for other types of predictor variables or conditions as well as other categories of indexes or indicators for the dependent variables.

In a similar way, the method could be applied in the field of the indoor air quality monitoring from residential, industrial, or office buildings to evaluate the environmental effects on the population health or “critical load” issue to evaluate the impact on ecosystems.

Acknowledgment

The authors would like to thank all those who contributed to this study.

Funding

This study was financially supported by the Core Program from the Ministry of Education and Research of Romania.

Additional information

Funding

This study was financially supported by the Core Program from the Ministry of Education and Research of Romania.

Notes on contributors

Elena Bucur

Elena Bucur is head of the pollution control department, National Research and Development Institute for Industrial Ecology–INCD ECOIND, Bucharest, Romania.

Andrei Florin Danet

Andrei Florin Danet is a research professor at the Department of Analytical Chemistry, University of Bucharest, Bucharest, Romania.

Carol Blaziu Lehr

Carol Blaziu Lehr is a researcher at the National Research and Development Institute for Industrial Ecology–INCD ECOIND, Bucharest, Romania.

Elena Lehr

Elena Lehr is head of the restoration department, Romanian National Aviation Museum, Bucharest, Romania.

Mihai Nita-Lazar

Mihai Nita-Lazar is a researcher at the National Research and Development Institute for Industrial Ecology–INCD ECOIND, Bucharest, Romania.