• No results found

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job are more likely to consume greater quantities of housing attributes. The results are consistent with those obtained by Blomquist and Worley (1981, 1982), and Witte, Sumka and Erekson (1979). The effect of occupation on housing consumption is generally positive but this tends to vary depending on the type and nature of occupation. For instance, public salaried workers tend to live in rented apartments than both self-employed and private-salaried workers. The choice made of residential housing also varies from one occupation to another.

Religion may be a factor in the emergence of residential concentrations as people who share cultural backgrounds including religion seek to live near each other or are attracted by services provided by religious organisations. In addition, religion may be used as a dimension in the identification of residential concentrations of people.

People of the same ethnic group are more alike, while people of different ethnic groups within the same racial group may be quite different. This suggests that individuals are drawn more to people of their own ethnic group rather than to people of other ethnic groups in the same racial group. In other words, people choose residences based on proximity to co-ethnics rather than other co-racial, but since all co-co-ethnics are of the same race, both ethnicity- and race-based concentration results. For instance, social capital theories suggest that ethnicity and race form important social and economic networks, leading people to gravitate towards others in the same group and ultimately resulting in geographic concentration by race and ethnicity. Thus, people will move to a neighbourhood or a place where there is a large population of coethnics.

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The raw data used was worked upon to suit the purpose of the study. For instance, data of over 826 variables were collected covering a variety of topics just like earlier mentioned above but those eventually used for the study were about 126 having undergone the data cleaning process . Importantly, the classification of the residential density areas was done in collaboration with the Lagos State staff of the department of budget and planning section of the secretariat. The Table for the classification is shown below:

Classification of the Local Governments in Residential Density Areas

Density is referred to as the number of persons, objects per unit of space, such as the number of persons or houses per acre or hectare. In housing literature, residential densities can be expressed in any of the following ways namely: (a) population density: the number of persons per acre or hectare; (b) Occupancy rate: the number of persons resident per habitable room;

(c) Housing density: the number of houses per acre or hectare; (iv) Accommodation density:

the number of habitable rooms per acre or hectare; (v) Bedspace density: the number of bedspaces per acre or hectare and (vi) Floor space rate: the amount of floor space (in square metres or square feet) per person.

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Table 5.3: LAGOS STATE RESIDENTIAL DENSITY CLASSIFICATION

S/N Local

Government Area

2006 High

Residential Area

Medium Residential Area

Low Residential Area

1. AGEGE 1,033,064

2. AJEROMI/IFELO

DUN

1,435,295

3. ALIMOSHO 2,047,026

4. AMUWO/ODOFI

N

524,971

5. APAPA 522,384

6. BADAGRY 380,420

7. EPE 323,634

8. ETI-OSA 983,515

9. IBEJU-LEKKI 99,540

10. IFAKO-IJAIYE 744,323

11. IKEJA 648,720

12. IKORODU 689,045

13. KOSOFE 934,614

14. LAGOS ISLAND 859,849

15. LAGOS

MAINDLAND

629,469

16. MUSHIN 1,321,517

17. OJO 941,523

18. OSHODI/ISOLO 1,134,548

19. SHOMOLU 1,025,123

20 SURULERE 1,274,362

TOTAL 17,552,942 6 8 6

Note: population density per LG (population divided by landmass) was actually used to classify the residential areas into high, medium and low residential areas respectively.

114 5.6 ESTIMATION TECHNIQUES

The thesis employs choice-based model to estimate residential housing choice. It has been found appropriate to capture the central focus of this study which is: to determine empirically the factors determining the residential choice decision, because it is based on the analysis of both qualitative and quantitative data which is derived from a discrete choice specification of the demand for residential housing from a utility theoretical model. Discrete choice decisions10 in the context of random utility theory are usually modelled and estimated with the multinomial logit model (MNL) (Guadagni and Little, 1983). The multinomial logistic regression model used is generally effective where the dependent variable is composed of a polychotomous11 category having multiple choices. The basic concept was generalised from binary logistic regression (Aldrich & Nelson 1984, Hosmer & Lemeshow, 2000).

The MLM appeals to this study for three reasons. First, data for the study consist of individual specific characteristics, and the MLM is well-suitable to analyse the characteristics of the individual. If the data is composed of alternative specific attributes, then the conditional logit model (CLM) is appropriate. Second, while the MLM is most popular as discrete choice model, it has a strict restriction in use. An assumption of both MLM and CLM is that the alternatives are distinct and independent of one another. That is, introducing a new alternative leaves the relative odds of choosing among the existing alternatives unchanged.

This property is called the independence of irrelevant alternatives (IIA) assumption. The IIA assumption follows from the assumption that the stochastic disturbances are independent and identically distributed. However, if alternatives are close substitutes for one another, then the IIA assumption is violated. The MLM has suffered from the IIA assumption in many areas by restricting the correlation patterns among choice alternatives. The IIA assumption, however, can only be empirically tested when some respondents have different choice sets. That is, when everyone in the sample is presented with the same choice set, the IIA assumption is not a serious problem (Allison, 1999). For the study, six alternatives are presented to all individuals. Thus, this study is free from IIA assumption. In addition, the MLM is easy to estimate even for a large number of alternatives (Borsch-Supan, 1990). Third, one of the alternatives to the MLM is the nested logit model (NLM) developed by McFadden (1978),

10 Utility-based choice or choice based on the relative attractiveness of competing alternatives from a set of mutually exclusive alternatives is called a discrete choice situation.

11 Polychotomous logistic regression is frequently the method of choice when outcome is categorical (2 or more mutually exclusive, unordered response categories) and interest is in relationship between the outcome and covariates. The covariates may be binary, categorical, ordinal, or continuous.

115

which relaxes the IIA restriction of the MNL by allowing alternatives to be correlated across, but not within, groups (Greene, 2003). However, if a larger number of independent variables are included, the NLM is difficult to employ.

The basic framework for analysis is provided by the random utility model where consumers are assumed to choose among a range of discrete number of alternatives to maximise their utility.

Let an individual household i choose from a set of mutually exclusive alternatives

1, , .

j            J He/she obtains a certain level of utility Uij from each alternative. The discrete choice model is based on the principle that the individual household chooses the outcome that maximizes the utility. We do not observe his/her utility, but observe some attributes of the alternatives as faced by the household. This utility according to random utility theory can be decomposed into systematic and random components of utility. That is, total utility is the sum of observable and unobservable components, Hence, the utility is decomposed into deterministic V and random part ijij:

,

ij ij ij

UV  j.---(25)

Since ij is not observed, the household‘s choice cannot be predicted exactly. Instead, the probability of any particular outcome is derived. The unobserved term is treated as random with density (fij). The joint density of the random vector  ii1,,iJ is denoted ( )fi . Probability that household i chooses alternative j among J alternatives is

Pr( )

ij ij ik

PUU  j i

Pr(Vij ijVik  ik j i)

I V( ijij Vik  ik j i f) ( ) i d i--- (26) where I(.) is the indicator function, equaling 1 when the term in parenthesis is true and 0 otherwise. This is a multidimensional integral over the density of the unobserved portion of utility ( )fi . Different discrete choice models are obtained from different specifications of the density. The deterministic part V ij of utility is usually treated as a linear function of explanatory variables x and an unknown vector of underlying parameters. In random utility models the expectation of the random component E(ij)is assumed to equal 0, that in turn

116

implies (E Uij)Vij. A vector of utilities Uij,j is assumed to be continuously distributed with an existing covariance matrix (see Tutz, 2000).

The absolute level of utility in Equation 26 is irrelevant to the individual household behavior. For example, if a constant is added to the utility of all alternatives, the alternative with the highest utility does not change. The choice probability is

( ) ( 0),

ij ij ik ij ik

PP UUP UU  , which depends only on the difference in utility, not its absolute level. The fact that only differences in utility matter has several implications for the identification and specification of discrete choice models. In general it means that the only parameters that can be estimated (that is, are identified) are those that capture differences across alternatives. In order to investigate the way and how observed factors influence the individual household to make a choice, unknown parameters  of the model are estimated.

The log-likelihood estimator can be used to estimate the parameters. The log-likelihood function to be maximized over parameters  is given as :

1 1

ln ( ) ln

N J

ij ij

i j

Ly P

 

---(27) Where yijequals 1 if alternative j is chosen and equals 0 for all other non-chosen alternatives.

The multinomial logit (MNL) model, invented by McFadden (1974), is obtained by the assumption that each random components ij in the utilities (25) is distributed independently, identically type I extreme value, where the variance of the error term is equal to2/ 6. The density for each unobserved component of utility and the cumulative distribution are given, respectively, by

( )

ij

ij e

ij e e and

    ( ij)eeij ---(28) The random utility (25) is combined with the probability distribution for the random components ij in equation (28) and assumes independence among the random components of the different alternatives. The probability that an individual household i choose alternative j among the J alternatives is given by

Pij Pr(ijVijVik  ik j i)

Pr( ij ij ik ik ) ij

j k

V V j i d

  

 

    ---(29) Thus, the choice probability is the integral over all values of ijweighted by its density (.) as defined in (28). This integral has a closed form solution and after some manipulation the logit probabilities, with Vijxi'j,become:

'

'

i j

i k

x

ij x

j

P e

e

---(30)

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Since MNL is a model where regressors do not vary over choices, coefficients are estimated for any choice. MNL requires identification: one of the choices, say j, is treated as the base category (correspondent jis constrained to equal 0). Substitution of equation (30) into (27) yields the log-likelihood function to be maximized over parameters 

'

'

1 1

ln ( ) ln

i j

i k

N J x

ij x

i j

j

L y e

e

  

---(31) where yij equals 1 if alternative j is chosen and equals 0 for all other non-chosen alternatives (Greene, 2003).

Thus the study uses MLM to discern the determinants of the residential housing choice across different segments of population namely High, Medium and Low. The multinomial logistic regression model used in this study estimates the effect of the individual variables on the probability of choosing an alternative residential housing type. This is informed by the fact that an individual household in Nigeria may be found occupying or renting houses in any one of the six residential housing choice as obtainable in the Lagos State housing surveys. These residential choices are single household houses, multi-household houses, flats in a block of flats, duplex, room in the main building and squatters‘

settlements. The model can be expressed as follows:

,

1

exp( )

Pr[ ]

1 exp( , )

i j

h

ij j

i j

k

Q P X

X

 

---(32) where Qh=Pij is the dependent variable and the number of alternatives in the choice set. The model is estimated with six alternatives: j=1 if the respondents indicate they prefer single-household houses as their choice of residence; j=2 if the respondents indicate they prefer multi-household houses as their residential housing choice; j=3 if the respondents indicate flats in a block of flats as their residential housing choice; j=4 if the respondents indicate they prefer duplex as their choice of residence; j=5 if the respondents indicate they prefer room in the main building as their residential housing choice; j=6 if the respondents indicate they make choice of squatters‘ settlement as their residential choice12 . The second alternative, j=2,

12(i) Single household house – a whole building (bungalow) occupied by one household.

(ii) Multi-household house - a whole building (bungalow) occupied by more than one households.

(iii) Duplex - a storey building with inbuilt stair case occupied by a single household.

(iv) Room in the main building is defined as space occupied by a household in a building containing more than one room with shared toilets and kitchens.

(v) Flat in a block of flats- refer to flats in an estate and flats in more than one building with same designs and separate conveniences but share same address. The number of bedrooms is usually used to denote them e.g. 2 bedroom, 3 bedroom etc.

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show the respondents that indicated that they prefer multi-household houses as their residential housing choice, is used as the reference choice. The independent variables, Xi, hypothesised to influence the alternatives are summarised as follows: (1) transformed hedonic housing prices; (2) household incomes; and (3) socioeconomic and demographic factors. ßj is a vector of the estimated parameters, and Pr[Qh=Pij] is the probability of individual i choosing j alternative among six alternatives in the choice set.

Coefficients of the MLM are difficult to interpret because of the proliferation of parameters, which results in increased complexity in interpreting the estimates (Greene, 2003). The, marginal effects of the MLM are also difficult to derive.

The derivatives of the probabilities of the alternatives with respect to each of the explanatory variables are obtained at the sample means of the explanatory variables.

However, calculating marginal probabilities are not very useful to evaluate the magnitude of ß in MLM. First of all, discrete change represents the change for a particular set of values of the independent variables. Thus, the changes will not be the same at different levels of the variables. Another problem with marginal probability is that the dynamics among the dependent outcomes cannot be captured from measures of discrete change (Long, 1997). Therefore, for the study, results are interpreted using the odds ratio, which is the exponentiated coefficient. The odds ratio is calculated by contrasting each category with the reference category. The odds ratio shows a multiplicative change in the odds for a unit change in an independent variable. The logistic coefficient is interpreted as the change in the logit associated with a one unit change in the independent variable, holding all other variables constant. The exponential of the logistic coefficient is the effects on the odds rather than probability. In interpretation, a one unit change in the independent variable, tis expected to change the odds by a factor of exp(ß) when other things are equal.

The exponential of a positive number is greater than one, and the exponential of a negative number is less than one. Thus, the threshold between positive and negative effect is one in interpreting odds ratio. If exponentiated coefficient is greater than one, that implies increased odds. On the other hand, if exponentiated coefficient is between zero and one, odds decrease. The distance of exponentiated coefficient from one in either direction explains the size of the effect on the odds for unit change in the independent variable (Pampel, 2000).

(vi) Squatter’ Settlement- can be defined as a residential area which has developed without legal claims to the land and/or permission from the concerned authorities to build; as a result of their illegal or semi-legal status, infrastructure and services are usually inadequate

119 CHAPTER SIX

ANALYSIS AND INTERPRETATION OF RESULTS 6.1 Introduction

This chapter presents the analysis of housing characteristics and socio-demographic characteristics of the representative samples across the three residential density areas in Lagos State. Apart from the socio-demographic variables description, analyses of hedonic results are also presented for full sample and high, medium and low residential density areas.

The essence of the hedonic pricing approach is to show the qualities of housing structure that are implicitly embedded in the house rents people normally pay for. A section of the chapter also presents results of the multinomial logit models approach employed.